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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
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
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