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Congruence Subgroups and $H_2(SL_2(\mathcal{O}_{K,S}))$.

组织者

李京艳 , 普拉文·库马尔 , 吴杰

演讲者

Pedro Henrique Amorim Alves

时间

2026年08月27日 15:00 至 16:00

地点

A3-4-301

线上

Zoom 242 742 6089 (BIMSA)

摘要

The study of congruence subgroups has been central to recent developments in the integral homology of $SL_2(A)$. In this talk, I will present a technique that enables you to calculate the abelianization of subgroups whose commutator is a congruence subgroup. From this, we obtain an exact sequence that provides information about $H_2(SL_2(\mathcal{O}_{K,S}))$. We have also conjectured a connection between this homology group and values of the Dedekind zeta function, through a homological version of the Birch-Tate formula. This work was conducted in collaboration with Isadora V. Picinini, Bruno R. Ramos, and Thiago Veríssimo.