ミニワークショップ
大岡山数論幾何ミニワークショップ
- 概要
- 時期: 2025年11月7日(金)
集会形式: 対面による研究集会
- 場所: 東京科学大学 大岡山本館 H201号室
- プログラム
13:30--14:30
講演者: 千田雅隆（東京電機大学）
タイトル：Harder's conjecture and congruence of Siegel modular forms
アブストラクト：In this talk, we will introduce a result on the Harder's conjecture for
the congruence between the Hecke eigenvalues of vector valued
Siegel modular forms and elliptic modular forms.
We will also discuss on an application to Bloch-Kato conjecture for
elliptic modular forms. This is a joint work with H. Atobe, T. Ibukiyama,
H. Katsurada and T. Yamauchi.
15:00--16:00
講演者: 坂本龍太郎（筑波大学）
タイトル: On Homology Classes of Modular Curves
アブストラクト: For narrow ideal classes of a real quadratic field, one can define homology classes of modular curves. These homology classes are arithmetic objects, in the sense that the values of their pairings with cohomology classes arising from modular forms are related to special values of L-functions. In this talk, I will present recent results on the size of the subgroup generated by these homology classes. This talk is based on joint work with Hohto Bekki (Saga University).
16:30--17:30
講演者: Francesc Castella（University of California, Santa Barbara）
タイトル: On nonvanishing conjectures by Kolyvagin and Kurihara, and their refinements
アブストラクト: In 1991, Kolyvagin formulated a nonvanishing conjecture for the system of cohomology classes derived from Heegner points on rational elliptic curves over ring class fields. About 20 years later, Wei Zhang first proved Kolyvagin's conjecture in many cases, and formulated a refinement of Kolyvagin's conjecture. In the cyclotomic context, similar conjectures were formulated by Kurihara (in terms of modular symbols) and C.-H. Kim (in terms of Kolyvagin derivatives of Kato's Euler system). In this talk, I will outline a new proof of Kolyvagin's conjecture that removes most of the hypotheses in Wei Zhang's result, and also yields the first proof of the refined Kolyvagin's conjecture. With the same approach, we also obtain analogous results for Kurihara's conjecture and its refinement. Based on joint works with A. Burungale, G. Grossi, and C. Skinner.
- 問い合わせ先:
- 落合理（東京工業大学）mail: (familyname).t.1998@m.isct.ac.jp