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東京電機大学 東京千住キャンパス 5号館11階 51119B室
吉川 祥 氏 (東京理科大学)
重さ1のモジュラー形式のHecke体について
（楕円）モジュラー形式fに対して、そのFourier係数を有理数体に添加して得られる体をfのHecke体という。 本講演では、fが重さ1の正規化されたHecke固有新形式でexotic type（すなわち、fに付随するGalois表現の射影像がA_4,S_4, A_5のいずれかと同型）に対して、そのようなfのHecke体の分類について説明する。 更に、時間が許せば、fに付随するGalois表現の像の構造決定についても述べる。 この講演は、坂本龍太郎氏（筑波大学）との共同研究に基づく。
世話人: 千田 雅隆・並川健一
東京電機大学 東京千住キャンパス 5号館11階 51119B室
Francesc Castella 氏 (University of California, Santa Barbara)
On the rank one case of the Birch–Swinnerton-Dyer formula for CM elliptic curves
Let E be an elliptic curve defined over a number field F with complex multiplication by the ring of integers of an imaginary quadratic field K, and assume the Shimura condition that the extension of F generated by the torsion points of E be abelian over K. In this talk, I will discuss recent progress on the Birch–Swinnerton-Dyer formula for E in the case of analytic rank one using Iwasawa theory.
世話人: 千田 雅隆・並川健一
東京電機大学 東京千住キャンパス 5号館11階 51119B室
Dohyeong Kim 氏 (Seoul National University)
Arithmetic Chern-Simons action of Massey type
The arithmetic Chern-Simons action was introduced by Minhyong Kim in 2015, as a part of his program to pursue a formalism in number theory which is structurally similar to those in quantum field theories in mathematical physics. From arithmetician's point of view, it provides a succinct way to capture non-abelian invariants of Galois extensions. In this talk, we will discuss a special case of it, which we call the Chern-Simons action of Massey type. It is related to Massey products in Galois cohomology and extends existing notions of trilinear symbols in number theory.
世話人: 千田 雅隆・並川健一
東京電機大学 東京千住キャンパス 5号館11階 51119B室
Francesco Lemma 氏 (Université Paris Cité)
New result on Beilinson conjecture for GSp(4), endoscopic case
Beilinson conjecture relating higher regulators to non-critical values of motivic L-functions is one of the main open problems in arithmetic geometry. My talk will begin with a motivation and statement of the conjecture. Then, I will present a new result concerning some motives attached to endoscopic cuspidal automorphic representations of the symplectic group GSp(4), including the main ideas of the proof.
世話人: 千田雅隆・並川健一
東京電機大学 東京千住キャンパス 5号館11階 51119B室
Adeel Khan 氏 (Academia Sinica)
Microlocal ℓ-adic sheaves
For real and complex analytic manifolds, the microlocal refinement of sheaf theory developed by Kashiwara and Schapira gives a simple construction of singular support and characteristic cycles of sheaves. For nonsingular algebraic varieties in positive characteristic, singular support and characteristic cycles have been defined by Beilinson and Takeshi Saito, respectively. In this talk we will explain some aspects of étale or ℓ-adic versions of microlocal sheaf theory, through which we obtain another possible construction of singular support and characteristic cycles in positive characteristic. Time permitting, we may also discuss microlocalization of motivic sheaves.
世話人: 時本一樹
東京電機大学 東京千住キャンパス 5号館11階 51119B室
竹内 大智 氏 (東京科学大学)
Positive characteristic analogue of Kashiwara-Malgrange theorem
Let X be a smooth algebraic variety over the complex numbers and f be a function on it. There are several known constructions associated to f that measure the singularity of f^{-1}(0). In the context of D-modules, one can associate the Bernstein-Sato polynomial, or b-function, of f. On the other hand, in the context of constructible sheaves, we have the nearby cycles complex. The Kashiwara-Malgrange theorem states that the roots of the b-function determine the monodromy eigenvalues of the nearby cycles. In this talk, I would like to discuss a positive characteristic analogue of this result. This is a joint work with Eamon Quinlan-Gallego and Hiroki Kato.
世話人: 時本一樹
東京電機大学 東京千住キャンパス 5号館11階 51119B室
髙谷 悠太 氏 (東京大学)
Special affinoids in local Shimura varieties at depth zero
Starting from the work of Teruyoshi Yoshida, the explicit geometry of Lubin-Tate spaces has been studied to provide a concrete description of their cohomology. For example, Yoshida constructed special affinoids in Lubin-Tate spaces at depth zero whose reductions are Deligne-Lusztig varieties. In this talk, I will present a generalization of this construction to all hyperspecial basic local Shimura varieties. The key input is the prismatic description of the universal deformation due to Kazuhiro Ito. If time permits, I will provide an outlook on the generalization to positive depth.
世話人: 時本一樹