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BIMSA Topology Seminar
BIMSA Topology Seminar
Congruence Subgroups and $H_2(SL_2(\mathcal{O}_{K,S}))$.
Congruence Subgroups and $H_2(SL_2(\mathcal{O}_{K,S}))$.
Organizers
Speaker
Pedro Henrique Amorim Alves
Time
Thursday, August 27, 2026 3:00 PM - 4:00 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
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.