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11月8日(水) 18時
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X. Wan (万\UTF{6615}) (Morningside Center for Mathematics(中国科学院晨\UTF{5174}数学中心))

Iwasawa theory and Bloch-Kato conjecture for modular forms

Bloch and Kato formulated conjectures relating sizes of p-adic Selmer groups with special values of L-functions. Iwasawa theory is a useful tool for studying these conjectures and BSD conjecture for elliptic curves. For example the Iwasawa main conjecture for modular forms formulated by Kato implies the Tamagawa number formula for modular forms of analytic rank 0.
In this talk I'll first briefly review the above theory. Then we will focus on a different Iwasawa theory approach for this problem. The starting point is a recent joint work with Jetchev and Skinner proving the BSD formula for elliptic curves of analytic rank 1. We will discuss how such results are generalized to modular forms. If time allowed we may also explain the possibility to use it to deduce Bloch-Kato conjectures in both analytic rank 0 and 1 cases. In certain aspects such approach should be more powerful than classical Iwasawa theory, and has some potential to attack cases with bad ramification at p.

2017年12月13日(水) 18時
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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
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Ana Caraiani (Imperial College)

終わったもの