| Seminar information archive -05/16 | Future seminars 05/17- | Seminars | Graduate School of Mathematical Sciences | Access |
16:40 - 17:40Room #002 (Mathematics building)
Naoya Umezaki (University of Tokyo)
"On uniform bound of the maximal subgroup of the inertia group acting unipotently on $¥ell$-adic cohomology" (JAPANESE)
For a smooth projective variety over a local field,
the action of the inertia group on the $¥ell$-adic cohomology group is
unipotent if it is restricted to some open subgroup.
In this talk, we give a uniform bound of the index of the maximal open
subgroup satisfying this property.
This bound depends only on the Betti numbers of $X$ and certain Chern
numbers depending on a projective embedding of $X$.
16:40 - 17:40Room #056 (Mathematics building)
Alan Lauder (University of Oxford)
"Explicit constructions of rational points on elliptic curves" (ENGLISH)
I will present an algorithm for computing certain special
values of p-adic L-functions, and discuss an application to
the efficient construction of rational points on elliptic curves.
17:30 - 18:30Room #056 (Mathematics building)
Damian Rossler (CNRS, Universite de Toulouse)
"Around the Mordell-Lang conjecture in positive characteristic " (ENGLISH)
Let V be a subvariety of an abelian variety A over C and let G\subseteq A(C) be a subgroup. The classical Mordell-Lang conjecture predicts that if V is of general type and G\otimesQ is finite dimensional, then V\cap G is not Zariski dense in V. This statement contains the Mordell conjecture as well as the Manin-Mumford conjecture (for curves). The positive characteristic analog of the Mordell-Lang conjecture makes sense, when A is supposed to have no subquotient, which is defined over a finite field. This positive characteristic analog was proven in 1996 by E. Hrushovski using model-theoretic methods. We shall discuss the prehistory and context of this proof. We shall also discuss the proof (due to the speaker) of the fact that in positive characteristic, the Manin-Mumford conjecture implies the Mordell-Lang conjecture (whereas this seems far from true in characteristic 0).
18:00 - 19:00Room #056 (Mathematics building)
Takuro Mochizuki (Research Institute for Mathematical Sciences, Kyoto University)
"Twistor $D$-module and harmonic bundle" (ENGLISH)
Abstract:
We shall overview the theory of twistor $D$-modules and
harmonic bundles. I am planning to survey the following topics,
motivated by the Hard Lefschetz Theorem for semisimple holonomic
$D$-modules:
1. What is a twistor $D$-module?
2. Local structure of meromorphic flat bundles
3. Wild harmonic bundles from local and global viewpoints
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
18:15 - 19:15Room #056 (Mathematics building)
Toby Gee (Imperial College London)
"New perspectives on the Breuil-Mézard conjecture (joint with M. Emerton) " (ENGLISH)
I will discuss joint work with Matthew Emerton on geometric approaches to the Breuil-Mézard conjecture, generalising a geometric approach of Breuil and Mézard. I will discuss a proof of the geometric version of the original conjecture, as well as work in progress on a geometric version of the conjecture which does not make use of a fixed residual representation.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 17:30Room #056 (Mathematics building)
Kazuya Kato (University of Chicago)
"On Sharifi's conjecture" (JAPANESE)
16:30 - 17:30Room #117 (Mathematics building)
Tamas Szamuely (Budapest)
"Galois Theory: Past and Present" (ENGLISH)
17:30 - 18:30Room #056 (Mathematics building)
Lucien Szpiro (City University of New York)
"Good and bad reduction for algebraic dynamical systems" (ENGLISH)
We will report on a recent work with collaborators in New York on the
different ways to look at degenerations of a dynamical system in a one
parameter family. Resultants, conductors and isotriviality will be analyzed.
18:30 - 19:30Room #056 (Mathematics building)
Gerd Faltings (Max Planck Institute for Mathematics, Bonn)
"Nonabelian p-adic Hodge theory and Frobenius" (ENGLISH)
Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
18:00 - 19:00Room #056 (Mathematics building)
Atsushi Shiho (University of Tokyo)
"On extension and restriction of overconvergent isocrystals " (ENGLISH)
First we explain two theorems concerning (log) extension of overconvergent isocrystals. One is a p-adic analogue of the theorem of logarithmic extension of regular integrable connections, and the other is a p-adic analogue of Zariski-Nagata purity. Next we explain a theorem which says that we can check certain property of overconvergent isocrystals by restricting them to curves.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 17:30Room #056 (Mathematics building)
Kensaku Kinjo (University of Tokyo)
"Hypergeometric series and arithmetic-geometric mean over 2-adic fields" (JAPANESE)
Dwork proved that the Gaussian hypergeometric function on p-adic numbers
can be extended to a function which takes values of the unit roots of
ordinary elliptic curves over a finite field of characteristic p>2.
We present an analogous theory in the case p=2.
As an application, we give a relation between the canonical lift
and the unit root of an elliptic curve over a finite field of
characteristic 2
by using the 2-adic arithmetic-geometric mean.
17:30 - 18:30Room #056 (Mathematics building)
Andrei Suslin (Northwestern University)
"K_2 of the biquaternion algebra" (ENGLISH)
http://www.ihes.fr/~abbes/SGA/suslin.pdf
16:00 - 18:15Room #123 (Mathematics building)
Takeshi Saito (University of Tokyo) 16:00 - 17:00
"Discriminants and determinant of a hypersurface of even dimension" (ENGLISH)
The determinant of the cohomology of a smooth hypersurface
of even dimension as a quadratic character of the absolute
Galois group is computed by the discriminant of the de Rham
cohomology. They are also computed by the discriminant of a
defining polynomial. We determine the sign involved by testing
the formula for the Fermat hypersurfaces.
This is a joint work with J-P. Serre.
Dennis Eriksson (University of Gothenburg) 17:15 - 18:15
"Multiplicities of discriminants" (ENGLISH)
The discriminant of a homogenous polynomial is another homogenous
polynomial in the coefficients of the polynomial, which is zero
if and only if the corresponding hypersurface is singular. In
case the coefficients are in a discrete valuation ring, the
order of the discriminant (if non-zero) measures the bad
reduction. We give some new results on this order, and in
particular tie it to Bloch's conjecture/the Kato-T.Saito formula
on equality of localized Chern classes and Artin conductors. We
can precisely compute all the numbers in the case of ternary
forms, giving a partial generalization of Ogg's formula for
elliptic curves.
17:30 - 18:30Room #056 (Mathematics building)
Tomoyuki Abe (IPMU)
"Product formula for $p$-adic epsilon factors " (ENGLISH)
I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.
16:30 - 17:30Room #056 (Mathematics building)
Yuichi Hirano (University of Tokyo)
"Congruences of modular forms and the Iwasawa λ-invariants" (JAPANESE)
17:00 - 18:00Room #056 (Mathematics building)
Yuya Matsumoto (University of Tokyo)
"On good reduction of some K3 surfaces" (JAPANESE)
16:30 - 17:30Room #056 (Mathematics building)
Masaki Nishimoto (University of Tokyo)
"On the linear independence of values of some Dirichlet series" (JAPANESE)
17:30 - 18:30Room #056 (Mathematics building)
Michel Raynaud (Universite Paris-Sud)
"Permanence following Temkin" (ENGLISH)
When one proceeds to a specialization, the good properties of algebraic equations may be destroyed. Starting with a bad specialization, one can try to improve it by performing modifications under control. If, at the end of the process, the initial good properties are preserved, one speaks of permanence. I shall give old and new examples of permanence. The new one concerns the relative semi-stable reduction of curves recently proved by Temkin.
16:30 - 17:30Room #056 (Mathematics building)
Yuuki Takai (University of Tokyo)
"An analogue of Sturm's theorem for Hilbert modular forms" (JAPANESE)
11:00 - 12:00Room #056 (Mathematics building)
Joseph Ayoub (University of Zurich)
"The motivic Galois group and periods of algebraic varieties" (ENGLISH)
We give a construction of the motivic Galois group of $\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.
16:30 - 17:30Room #056 (Mathematics building)
Shinichi Kobayashi (Tohoku University)
"The p-adic Gross-Zagier formula for elliptic curves at supersingular primes " (JAPANESE)
The p-adic Gross-Zagier formula is a formula relating the derivative of the p-adic L-function of elliptic curves to the p-adic height of Heegner points. For a good ordinary prime p, the formula is proved by B. Perrin-Riou more than 20 years ago. Recently, the speaker proved it for a supersingular prime p. In this talk, he explains the proof.
16:30 - 18:45Room #056 (Mathematics building)
Zhonghua Li (University of Tokyo) 16:30 - 17:30
"On regularized double shuffle relation for multiple zeta values" (ENGLISH)
Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.
Dan Yasaki (North Carolina University) 17:45 - 18:45
"Spines with View Toward Modular Forms" (ENGLISH)
The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of
its action on the upper half plane. In this talk, we will examine spines, which are the ``smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.
16:30 - 17:30Room #056 (Mathematics building)
Takashi Hara (University of Tokyo)
"Inductive construction of the p-adic zeta functions for non-commutative p-extensions of totally real fields with exponent p" (JAPANESE)
We will discuss how to construct p-adic zeta functions and verify
the main conjecture in special cases in non-commutative Iwasawa theory
for totally real number fields.
The non-commutative Iwasawa main conjecture for totally real number
fields has been verified in special cases by Kazuya Kato,
Mahesh Kakde and the speaker by `patching method of p-adic zeta functions'
introduced by David Burns and Kazuya Kato (Jurgen Ritter and Alfred Weiss
have also constructed the successful example of the main conjecture
under somewhat different formulations).
In this talk we will explain that we can prove the main conjecture
for cases where the Galois group is isomorphic
to the direct product of the ring of p-adic integer and a finite p-group
of exponent p by utilizing Burns-Kato's method and inductive arguments.
Finally we remark that in 2010 Ritter-Weiss and Kakde independently
justified the non-commutative main conjecture
for totally real number fields under general settings.
16:30 - 18:45Room #056 (Mathematics building)
Yuichiro Hoshi (RIMS, Kyoto University) 16:30 - 17:30
"On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves" (JAPANESE)
In this talk, we will discuss the following problem posed by Makoto Matsumoto and Akio Tamagawa concerning monodromic fullness of hyperbolic curves.
For a hyperbolic curve X over a number field, are the following three conditions equivalent?
(A) For any prime number l, X is quasi-l-monodromically full.
(B) There exists a prime number l such that X is l-monodromically full.
(C) X is l-monodromically full for all but finitely many prime numbers l.
The property of being (quasi-)monodromically full may be regarded as an analogue for hyperbolic curves of the property of not admitting complex multiplication for elliptic curves, and the above equivalence may be regarded as an analogue for hyperbolic curves of the following result concerning the Galois representation on the Tate module of an elliptic curve over a number field proven by Jean-Pierre Serre.
For an elliptic curve E over a number field, the following four conditions are equivalent:
(0) E does not admit complex multiplication.
(1) For any prime number l, the image of the l-adic Galois representation associated to E is open.
(2) There exists a prime number l such that the l-adic Galois representation associated to E is surjective.
(3) The l-adic Galois representation associated to E is surjective for all but finitely many prime numbers l.
In this talk, I will present some results concerning the above problem in the case where the given hyperbolic curve is of genus zero. In particular, I will give an example of a hyperbolic curve of type (0,4) over a number field which satisfies condition (C) but does not satisfy condition (A).
Marco Garuti (University of Padova) 17:45 - 18:45
"Galois theory for schemes" (ENGLISH)
We discuss some aspects of finite group scheme actions: the Galois correspondence and the notion of Galois closure.
16:30 - 17:30Room #056 (Mathematics building)
Shin Harase (University of Tokyo)
"Fast lattice reduction for F_2-linear pseudorandom number generators" (JAPANESE)
16:30 - 17:30Room #117 (Mathematics building)
Hélène Esnault (Universität Duisburg-Essen)
"Finite group actions on the affine space" (ENGLISH)
If $G$ is a finite $\ell$-group acting on an affine space $\A^n$ over a
finite field $K$ of cardinality prime to $\ell$, Serre shows that there
exists a rational fixed point. We generalize this to the case where $K$ is a
henselian discretely valued field of characteristic zero with algebraically
closed residue field and with residue characteristic different from $\ell$.
We also treat the case where the residue field is finite of cardinality $q$
such that $\ell$ divides $q-1$. To this aim, we study group actions on weak
N\'eron models.
(Joint work with Johannes Nicaise)
16:30 - 17:30Room #056 (Mathematics building)
Takahiro Tsushima (University of Tokyo)
"On the stable reduction of $X_0(p^4)$" (JAPANESE)
16:30 - 17:30Room #056 (Mathematics building)
Luc Illusie (Universite de Paris-Sud)
"Vanishing theorems revisited, after K.-W. Lan and J. Suh" (ENGLISH)
Let k be an algebraically closed field of characteristic p and X,
Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar
type for certain nef and big line bundles L on Y and morphisms f : X -> Y
having semistable reduction along a divisor with simple normal crossings. It
holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2
and dimension assumptions, and generalizes vanishing theorems of Esnault-
Viehweg and of mine. I'll give an outline of the proof and sketch some
applications, due to K.-W. Lan and J. Suh, to the cohomology of certain
automorphic bundles arising from PEL type Shimura varieties.
16:15 - 17:15Room #052 (Mathematics building)
Richard Hain (Duke University)
"Universal mixed elliptic motives" (ENGLISH)
This is joint work with Makoto Matsumoto. A mixed elliptic
motive is a mixed motive (MHS, Galois representation, etc) whose
weight graded quotients are Tate twists of symmetric powers of the the
motive of elliptic curve. A universal mixed elliptic motive is an
object that can be specialized to a mixed elliptic motive for any
elliptic curve and whose specialization to the nodal cubic is a mixed
Tate motive. Universal mixed elliptic motives form a tannakian
category. In this talk I will define universal mixed elliptic motives,
give some fundamental examples, and explain what we know about the
fundamental group of this category. The "geometric part" of this group
is an extension of SL_2 by a prounipotent group that is generated by
Eisenstein series and which has a family of relations for each cusp
form. Although these relations are not known, we have a very good idea
of what they are, thanks to work of Aaron Pollack, who determined
relations between the generators in a very large representation of
this group.
17:30 - 18:30Room #056 (Mathematics building)
Fabrice Orgogozo (CNRS, École polytechnique)
"Constructibilité uniforme des images directes supérieures en cohomologie étale " (ENGLISH)
Motivé par une remarque de N. Katz sur le lien entre la
torsion de la Z_ℓ-cohomologie étale et les ultraproduits de groupes de
F_ℓ-cohomologie, nous démontrons un théorème d'uniformité en ℓ pour la
constructibilité des images directes supérieures entre schémas de type fini
sur un trait excellent. (Un tel théorème avait été considéré par
O. Gabber il y a plusieurs années déjà.)
La méthode est maintenant classique : on utilise des
théorèmes de A. J. de Jong et un peu de log-géométrie.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted from IHES by the internet.)
16:30 - 17:30Room #056 (Mathematics building)
Ryoko Tomiyasu (KEK)
"On some algebraic properties of CM-types of CM-fields and their reflex fields" (JAPANESE)
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.
For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \rtimes S_n$.
Using properties of the embedding, a set of CM-types $\Phi$ of $K$ and their
dual CM-types $(K, \Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual
CM-type.
I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.
17:30 - 18:30Room #056 (Mathematics building)
Makoto Matsumoto (University of Tokyo)
"Differences between Galois representations in outer-automorphisms of the fundamental groups and those in automorphisms, implied by topology of moduli spaces" (ENGLISH)
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number field K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:
ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).
Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are infinitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.
This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).
There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)
17:30 - 18:30Room #056 (Mathematics building)
Gerard Laumon (CNRS, Universite Paris XI - Orsay)
"The cohomological weighted fundamental lemma "
Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 18:45Room #056 (Mathematics building)
津嶋 貴弘 (東京大学大学院数理科学研究科) 16:30 - 17:30
"Elementary computation of ramified component of the Jacobi sum"
R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.
Christopher Deninger (Universität Münster) 17:45 - 18:45
"P-divisible groups and the p-adic Corona problem"
16:30 - 17:30Room #056 (Mathematics building)
Bernard Le Stum (Université de Rennes 1)
"The local Simpson correspondence in positive characteristic"
A Simpson correspondance should relate Higgs bundles to differential modules (or local systems). We stick here to positive characteristic and recall some old and recent results : Cartier isomorphism, Van der Put's classification, Kaneda's theorem and Ogus-Vologodsky local theory. We'll try to explain how the notion of Azumaya algebra is a convenient tool to unify these results. Our main theorem is the equivalence between quasi-nilpotent differential modules of level m and quasi-nilpotent Higgs Bundles (depending on a lifting of Frobenius mod p-squared). This result is a direct generalization of the previous ones. The main point is to understand the Azumaya nature of the ring of differential operators of level m. Following Berthelot, we actually use the dual theory and study the partial divided power neighborhood of the diagonal.
16:30 - 17:30Room #056 (Mathematics building)
Ahmed Abbes (Université de Rennes 1)
"On GAGA theorems for the rigide-étale topology"
Last year, I finished my course in Todai on "Rigide Geometry following M. Raynaud" by stating a GAGA theorem for the rigide-étale topology, due to Gabber and Fujiwara. I will give a new proof of this theorem, inspired by another theorem of Gabber, namely the Affine analog of the proper base change theorem.
11:00 - 12:00Room #123 (Mathematics building)
Dinakar Ramakrishnan (カリフォルニア工科大学)
"Modular forms and Calabi-Yau varieties"
16:30 - 17:30Room #117 (Mathematics building)
Fabien Trihan (Nottingham大学)
"On the $p$-parity conjecture in the function field case"
Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).
16:30 - 18:45Room #056 (Mathematics building)
Vincent Maillot (Paris第7大学) 16:30 - 17:30
"New algebraicity results for analytic torsion"
Richard Hain (Duke大学) 17:45 - 18:45
"On the Section Conjecture for the universal curve over function fields"
16:30 - 18:30Room #056 (Mathematics building)
Bruno Kahn (Paris第7大学)
"On the classifying space of a linear algebraic group"
16:30 - 18:30Room #056 (Mathematics building)
Bruno Kahn (Paris第7大学)
"Motives and adjoints"
16:30 - 17:30Room #056 (Mathematics building)
Gombodorj Bayarmagnai (東京大学大学院数理科学研究科)
"The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2)"
16:30 - 17:30Room #056 (Mathematics building)
廣江 一希 (東京大学大学院数理科学研究科)
"Generalized Whittaker functions for degenerate principal series of GL(4,R) "
16:30 - 18:45Room #056 (Mathematics building)
大久保 俊 (東京大学大学院数理科学研究科) 16:30 - 17:30
"剰余体が非完全な場合のB_dR^+のGalois理論"
斎藤 秀司 (東京大学大学院数理科学研究科) 17:45 - 18:45
"A counterexample of Bloch-Kato conjecture over a local field and infinite torsion in algebraic cycles of codimension two"
16:30 - 17:30Room #056 (Mathematics building)
Pierre Colmez (École polytechnique)
"On the p-adic local Langlands correspondence"
16:30 - 17:30Room #056 (Mathematics building)
鈴木正俊 (東京大学大学院数理科学研究科)
"Mean-periodicity and analytic properties of zeta-functions"
Mean-periodicityというのは周期性の概念のひとつの一般化である。最近、I. Fesenko, G. Ricottaとの共同研究により、数論的スキームのゼータ関数を含むある複素関数のクラスと、mean-periodicityとの関連性が新しく見出された。
これはHecke-Weilによる, 解析接続と関数等式を持つDirichlet級数と保型形式との対応の一つの拡張ともみなせる. この背景には, I. Fesenkoの高次元アデール上のゼータ積分の理論があり、数論的スキームのHasseゼータ関数の解析接続を高次元アデール上の調和解析から導こうというプログラムの一環となっている。
この講演ではそのような背景にも若干触れた上、ゼータ関数の解析的性質とmean-periodicityの関連、特に解析接続と関数等式との関連について解説する。
16:30 - 17:30Room #056 (Mathematics building)
平田典子 (日本大学理工学部)
"Lang's Observation in Diophantine Problems"
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\varphi$ be a rational function on $E$. Then, for every point $P\in E(K)$ where $\varphi$ does not vanish at $P$, the logarithms of a norm of $\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.
16:30 - 17:30Room #056 (Mathematics building)
Olivier Fouquet (大阪大学)
"Dihedral Iwasawa theory of ordinary modular forms"
According to Hida theory, the Galois representation attached to a nearly-ordinary Hilbert eigencuspform belongs to a p-adic analytic family of Galois representations parametrized by varying weights. After restricting it to the absolute Galois group of a quadratic totally complex extension, it also belongs to a p-adic family coming from classical dihedral Iwasawa theory. We will explain the proofs of part of the main conjecture in Iwasawa theory in these situations, i.e divisibilities of characteristic ideals when equalities are actually expected.
16:30 - 17:30Room #056 (Mathematics building)
Daniel Caro (Université de Caen)
"Overholonomicity of overconvergence $F$-isocrystals on smooth varieties"
Let $¥mathcal{V}$ be a complete discrete valuation ring
of characteristic $0$, with perfect residue field $k$ of
characteristic $p>0$. In order to construct $p$-adic coefficients
over $k$-varieties, Berthelot introduced the theory of
overconvergent $F$-isocrystals, i.e overconvergent isocrystals with
Frobenius structure. Moreover, to get a $p$-adic cohomology over
$k$-varieties stable under cohomological operations, Berthelot built
the theory of arithmetic $F$-$¥mathcal{D}$-modules. In this talk,
after recalling some elements of these theories, we introduce the
notion of overholonomicity with is a property as stable as the
holonomicity in the classical theory of $¥mathcal{D}$-modules. The
goal of the talk is to prove the overholonomicity of arithmetic
$¥mathcal{D}$-modules associated to overconvergent $F$-isocrystals
over smooth $k$-varieties. In the proof we need Christol's transfert
theorem, a comparison theorem between relative log rigid cohomology
and relative rigid cohomology and last but not least Kedlaya's
semistable reduction theorem. This is a joint work with Nobuo
Tsuzuki.
16:30 - 17:30Room #056 (Mathematics building)
Pierre Parent (Universite Bordeaux 1)
"Serre's uniformity in the split Cartan case"
We show that, for large enough prime number p, the modular curve
X_{split}(p) has no other point with values in Q than CM points and the rational cusp. This gives a partial answer to an old question of J.-P. Serre concerning the uniform surjectivity of Galois representations associated to torsion points on elliptic curves without complex multiplication.
(Joint work with Yuri Bilu.)
16:30 - 17:30Room #117 (Mathematics building)
Christopher Deninger (Munster大学)
"A determinant for p-adic group algebras"
For a discrete countable group G there is a classical determinant on the units of the L^1-convolution algebra of G. It is defined using functional analysis and can be used for example to calculate the entropy of certain G-actions. We will discuss a p-adic analogue of this theory. Instead of functional analysis the definition of the p-adic determinant uses algebraic K-theory. It has an application to the study of the p-adic distribution of periodic G-orbits in certain G-action.
16:30 - 17:30Room #117 (Mathematics building)
Don Zagier (Max Planck研究所)
"$q$-series and modularity"
13:00 - 18:00Room #002 (Mathematics building)
Olivier Brinon (Paris北大学) 13:00 - 14:00
"B_dR-representations and Higgs bundles"
Henrik Russell (Duisburg-Essen大学) 14:15 - 15:15
"Generalized Albanese and duality"
Thomas Geisser (南California大学) 15:45 - 16:45
"Negative K-theory, homotopy invariance and regularity"
The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
Fabien Trihan (Nottingham大学) 17:00 - 18:00
"On Iwasawa theory for abelian varieties over function fields of positive characteristic"
16:30 - 17:30Room #117 (Mathematics building)
Valentina Di Proietto (Padova大学)
"On p-adic differential equation on semi-stable varieties "
16:30 - 17:30Room #117 (Mathematics building)
近藤 智 (東京大学数物連携宇宙研究機構)
"有限体上のスキームのふたつのモチビックコホモロジー群の計算 (安田正大氏との共同研究)"
16:30 - 18:45Room #117 (Mathematics building)
服部 新 (北海道大学大学院理学研究院) 16:30 - 17:30
"On a ramification bound of semi-stable torsion representations over a local field"
朝倉 政典 (北海道大学大学院理学研究院) 17:45 - 18:45
"Beilinson-Tate予想と楕円曲面のK_1の不分解元"
(佐藤周友氏との共同研究)
代数サイクルのTate予想のK理論における類似であるBeilinson-Tate予想について、
楕円曲面の場合にそれが成り立つ非自明な例を構成する。
これは、p進レギュレーターの非消滅と関係しており、
応用としてK_1の不分解元であって整数環上のモデルからくるようなものを構成する。
16:30 - 17:30Room #117 (Mathematics building)
坂内 健一 (慶應義塾大学理工学部 )
"$p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure (joint work with G. Kings) "
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.
16:30 - 17:30Room #117 (Mathematics building)
今井 直毅 (東京大学大学院数理科学研究科)
"On the connected components of moduli spaces of finite flat models"
16:30 - 17:30Room #117 (Mathematics building)
原 隆 (東京大学大学院数理科学研究科)
"Iwasawa theory of totally real fields for certain non-commutative $p$-extensions "
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.
16:30 - 17:30Room #117 (Mathematics building)
Luc Illusie (Universite Paris-Sud 11)
"Odds and ends on finite group actions and traces"
Suppose a finite group G acts on a scheme X separated and of finite type over a field k. This raises several questions about the traces of elements s of G (or more generally products sg, for g in the Galois group of k) on cohomology groups of various types associated with X/k (with compact support or no support, Betti if k = C, l-adic, rigid). Some were considered and solved long ago, others only recently. I will in particular discuss an equivariant generalization of a theorem of Laumon on Euler-Poincar¥'e characteristics.
16:30 - 17:30Room #117 (Mathematics building)
Weizhe Zheng (Universite Paris-Sud 11)
"Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields"
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
16:30 - 17:30Room #117 (Mathematics building)
Antoine Chambert-Loir (Universite de Rennes 1)
"Equidistribution theorems in Arakelov geometry"
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.
16:30 - 17:30Room #117 (Mathematics building)
中村健太郎 (東京大学大学院数理科学研究科)
"Classification of two dimensional trianguline representations of p-adic fields"
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\varphi, \Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\varphi,\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
16:30 - 17:30Room #117 (Mathematics building)
Christopher Rasmussen (京都大学数理解析研究所)
"Abelian varieties with constrained torsion"
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\Q$.
16:30 - 17:30Room #117 (Mathematics building)
Pierre Colmez (Ecole Polytechnique)
"On the p-adic local Langlands correspondance for GL2(Qp)"
16:30 - 17:30Room #117 (Mathematics building)
阿部知行 (東京大学大学院数理科学研究科)
"l進層のSwan導手とunit-root overconvergent F-isocrystalの特性サイクルについて"
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。
16:30 - 17:30Room #117 (Mathematics building)
James Lewis (University of Alberta)
"Abel-Jacobi Maps Associated to Algebraic Cycles I "
This talk concerns the Bloch cycle class map from the higher Chow groups to Deligne cohomology of a projective algebraic manifold. We provide an explicit formula for this map in terms of polylogarithmic type currents.
16:30 - 17:30Room #117 (Mathematics building)
Gereon Quick (Universitaet Muenster)
"Etale cobordism"
We define and study a new candidate of etale topological cohomology theories for schemes over a field of abritrary characteristic: etale cobordism. As etale K-theory is related to algebraic K-theory, etale cobordism is related to algebraic cobordism of Voevodsky and Levine/Morel. It shares some nice properties of topological theories, e.g. it is equipped with an Atiyah-Hirzebruch spectral sequence from etale cohomology. We discuss in particular a comparison theorem between etale and algebraic cobordism after inverting a Bott element and, finally, we give an outlook to further possible applications of this theory.
15:00 - 18:00Room #117 (Mathematics building)
E. Lau (Univ. of Bielefeld) 15:00 - 15:45
"Classification of p-divisible groups by displays and duality"
T. Zink (Univ. of Bielefeld) 16:00 - 16:45
"Applications of the theory of displays"
E. Looijenga (Univ. of Utrecht) 17:00 - 18:00
"Presentation of mapping class groups from algebraic geometry"
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.
16:30 - 17:30Room #002 (Mathematics building)
Steven Zucker (Johns Hopkins大学)
"The reductive Borel-Serre motive"
16:30 - 17:30Room #117 (Mathematics building)
梶原 健 (横浜国立大学)
"Tropical toric varieties"
16:30 - 17:30Room #117 (Mathematics building)
Andreas Rosenschon (University of Alberta)
"Algebraic cycles on products of elliptic curves over p-adic fields "
16:30 - 17:30Room #117 (Mathematics building)
Stephen Lichtenbaum (Brown University)
"The conjecture of Birch and Swinnerton-Dyer is misleading"
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.
16:30 - 17:30Room #117 (Mathematics building)
宮崎 直 (東京大学大学院数理科学研究科)
"$(g,K)$-module structures of principal series representations of $Sp(3,R)$"
16:30 - 17:30Room #117 (Mathematics building)
長谷川 泰子 (東京大学大学院数理科学研究科)
"Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields "
16:30 - 17:30Room #117 (Mathematics building)
津嶋 貴弘 (東京大学大学院数理科学研究科)
"Localized Characteristic Class and Swan Class"
16:30 - 17:30Room #117 (Mathematics building)
斎藤 毅 (東京大学大学院数理科学研究科)
"l進層の暴分岐と特性サイクル"
15:15 - 18:45Room #117 (Mathematics building)
Dennis Eriksson (東大数理/Paris) 15:15 - 16:15
"Towards a proof of a metrized Deligne-Riemann-Roch theorem"
小林 真一 (名古屋大学多元数理) 16:30 - 17:30
"CM楕円曲線の超特異点における2変数p進L関数 (A two variable p-adic L-function for CM elliptic curves at supersingular primes)"
Frans Oort (Utrecht) 17:45 - 18:45
"Irreducibility of strata and leaves in the moduli space of abelian varieties"
16:30 - 18:45Room #117 (Mathematics building)
Anna Cadoret (RIMS/JSPS) 16:30 - 17:30
"On the profinite regular inverse Galois problem"
Given a field $k$ and a (pro)finite group $G$, consider the
following weak version of the regular inverse Galois problem:
(WRIGP/$G$/$k$) \textit{there exists a smooth geometrically
irreducible curve $X_{G}/k$ and a Galois extension $E/k(X_{G})$
regular over $k$ with group $G$.} (the regular inverse Galois
problem (RIGP/$G$/$k$) corresponding to the case
$X_{G}=\mathbb{P}^{1}_{k}$). A standard descent argument shows that
for a finite group $G$ the (WRIGP/$G$/$k$) can be deduced from the
(RIGP/$G$/$k((T))$). For
profinite groups $G$, the (WRIGP/$G$/$k((T))$) has been proved for
lots of fields (including the cyclotomic closure of characteristic $0$
fields) but the descent argument no longer works.\
\indent Let $p\geq 2$ be a prime, then a profinite group
$G$ is said to be \textit{$p$-obstructed} if it fits in a profinite group extension
$$1\rightarrow K\rightarrow G\rightarrow G_{0}\rightarrow 1$$
with $G_{0}$ a finite group and $K\twoheadrightarrow
\mathbb{Z}_{p}$. Typical examples of such profinite groups $G$ are
universal $p$-Frattini covers of finite $p$-perfect groups or
pronilpotent projective groups.\
\indent I will show that the (WRIGP/$G$/$k$) - even under
its weaker formulation: (WWRIGP/$G$/$k$) \textit{there exists a
smooth geometrically irreducible curve $X_{G}/k$ and a Galois
extension $E/k(X_{G}).\overline{k}$ with group $G$ and field of
moduli $k$.} - fails for the whole class of $p$-obstructed profinite
groups $G$ and any field $k$ which is either a finitely generated
field of characteristic $0$ or a finite field of characteristic
$\not= p$.\
\indent The proof uses a profinite generalization of the cohomological obstruction
for a G-cover to be defined over its field of moduli and an analysis of the constrainsts
imposed on a smooth geometrically irreducible curve $X$ by a degree $p^{n}$
cyclic G-cover $X_{n}\rightarrow X$, constrainsts which are too rigid to allow the
existence of projective systems $(X_{n}\rightarrow
X_{G})_{n\geq 0}$ of degree $p^{n}$ cyclic G-covers
defined over $k$. I will also discuss other implicsations of these constrainsts
for the (RIGP).
Eric Friedlander (Northwestern) 17:45 - 18:45
"An elementary perspective on modular representation theory"
16:30 - 18:45Room #117 (Mathematics building)
Vincent Maillot (Jussieu/京大数理研) 16:30 - 17:30
"New applications of the arithmetic Riemann-Roch theorem"
Don Blasius (UCLA) 17:45 - 18:45
"Zariski Closures of Automorphic Galois Representations"
16:30 - 18:45Room #117 (Mathematics building)
G.Bayarmagnai (東大数理) 16:30 - 17:30
"Essential dimension of some finite group schemes"
Jacques Tilouine (パリ北大学) 17:45 - 18:45
"Overconvergent Siegel modular forms"
We recall what is known and what is conjectured on p-adic families of overconvergent Siegel modular forms. We show how this relates to a Fontaine-Mazur type conjecture on the classicality of certain overconvergent Siegel forms of genus 2. We explain few results known in this direction.
17:00 - 18:00Room #117 (Mathematics building)
平之内 俊郎 (九州大学)
"Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 )"
局所体の拡大とその付値環の或る商である"truncated" dvrの拡大の圏を比較する. 不分岐拡大と剰余体の拡大が一対一対応するのと同じ様に, 分岐に関する条件を加えれば,局所体と "truncated" dvr の拡大の圏が同値になる (Deligne).
今回は, 古典的な(上付き)分岐群の代わりにAbbes-斎藤による分岐群を用いて分岐に関する条件を与える. そして,この分岐群の Rigid 幾何的解釈を踏襲する事でDeligneの定理の剰余体が非完全な場合への一般化が得られる事を述べる.
16:30 - 18:45Room #117 (Mathematics building)
Fabrice Orgogozo (東大数理・Ecole Polytechnique de Paris) 16:30 - 17:30
"p-dimension of henselian fields: an application of Ofer Gabber's algebraization technique"
Kim Minhyong (Purdue大学・京大数理研) 17:45 - 18:45
"Fundamental groups and Diophantine geometry"
16:30 - 17:30Room #128 (Mathematics building)
Bas Edixhoven (Univ. of Leiden)
"Computation of the mod l Galois representations associated to Delta"
16:30 - 17:30Room #128 (Mathematics building)
A. Marmora (パリ北大・東大/学振)
"p-adic local constants"
16:30 - 17:30Room #117 (Mathematics building)
桜井 真 (東京大学理学系研究科)
"Beilinson-Drinfeld chiral algebra, geometric Langlands program and open Gromov-Witten invariants"
都合により、とりやめになりました。
16:30 - 17:30Room #117 (Mathematics building)
原下秀士 (北海道大学・学振)
"Configuration of the central streams in the moduli of abelian varieties"
16:30 - 17:30Room #117 (Mathematics building)
廣惠 一希 (東京大学大学院数理科学研究科)
"Hecke-Siegel's pull back formula for the Epstein zeta function with spherical"
16:30 - 18:45Room #117 (Mathematics building)
Kai Köehler (Düesseldorf 大学) 16:30 - 17:30
"Quaternionic analytic torsion and arithmetic geometry"
Thomas Geisser (南カリフォルニア大学) 17:45 - 18:45
"Duality via cycle complexes"
16:30 - 17:30Room #117 (Mathematics building)
伴 克馬 (東京大学大学院数理科学研究科)
"Differential Operators of Rankin-Cohen-Ibukiyama Type for Automorphic Forms of Several Variables"
16:30 - 17:30Room #117 (Mathematics building)
谷口 隆 (東京大学大学院数理科学研究科)
"Distributions of discriminants of cubic algebras"