東京北京パリ数論幾何セミナー
Seminaire de Geometrie Arithmetique Paris-Pekin-Tokyo, 巴黎北京東京算術幾何討論班

毎月第2水曜  056号室
午後5時半から6時半 (パリが夏時間のとき)  午後6時から7時 (パリが冬時間のとき) 
インターネットで、東大数理とIHES とMorningside centerで双方向同時中継します。

オーガナイザー: 志甫 淳、辻 雄、斎藤 毅、 Ahmed Abbes (CNRS, IHES), Fabrice Orgogozo (CNRS, Ecole Polytechnique), 田 野 (Tian Ye), 田 一超(Tian Yichao, Morningside center, HIM Bonn)、 鄭 維哲(Zheng Weizhe, Morningside center)
2017年12月13日(水) 18時

J. Fresán (Ecole Polytechnique)
Exponential motives

What motives are to algebraic varieties, exponential motives are to pairs (X, f) consisting of an algebraic variety over some field k and a regular function f on X. In characteristic zero, one is naturally led to define the de Rham and rapid decay cohomology of such pairs when dealing with numbers like the special values of the gamma function or the Euler constant gamma which are not expected to be periods in the usual sense. Over finite fields, the \UTF{00E9}tale and rigid cohomology groups of (X, f) play a pivotal role in the study of exponential sums. Following ideas of Katz, Kontsevich, and Nori, we construct a Tannakian category of exponential motives when k is a subfield of the complex numbers. This allows one to attach to exponential periods a Galois group that conjecturally governs all algebraic relations among them. The category is equipped with a Hodge realisation functor with values in mixed Hodge modules over the affine line and, if k is a number field, with an \UTF{00E9}tale realisation related to exponential sums. This is a joint work with Peter Jossen (ETH).
2018年1月17日(水) 18時

Ana Caraiani (Imperial College)
On the vanishing of cohomology for certain Shimura varieties

I will prove that the compactly supported cohomology of certain unitary or symplectic Shimura varieties at level Gamma_1(p^\infty) vanishes above the middle degree. The key ingredients come from p-adic Hodge theory and studying the Bruhat decomposition on the Hodge-Tate flag variety. I will describe the steps in the proof using modular curves as a toy model. I will also mention an application to Galois representations for torsion classes in the cohomology of locally symmetric spaces for GL_n. This talk is based on joint work in preparation with D. Gulotta, C.Y. Hsu, C. Johansson, L. Mocz, E. Reineke, and S.C. Shih.
終わったもの