Borel stability for congruence subgroups

TL;DR

This paper establishes a homological stability theorem for congruence subgroups of symplectic groups, generalizing Borel's theorem to show that specific homology groups are independent of the level of the subgroup.

Contribution

It proves a new homological stability result for symplectic congruence subgroups and extends Borel's theorem to a broader class of groups.

Findings

Homological stability for symplectic congruence subgroups

Homology groups independent of the congruence level

Generalization of Borel's theorem

Abstract

We prove a homological stability theorem for congruence subgroups of symplectic groups. From this theorem, we deduce a generalization of a theorem of Borel showing that certain homology groups of a congruence subgroup do not depend on the level of the congruence subgroup.