A torsion Jacquet--Langlands correspondence

TL;DR

This paper investigates the role of torsion in the homology of arithmetic groups and provides evidence linking it to the Langlands program, including a numerical Jacquet--Langlands correspondence in the torsion setting.

Contribution

It introduces a numerical form of the Jacquet--Langlands correspondence specifically for torsion in homology, advancing understanding in the Langlands program.

Findings

Evidence for torsion's role in the Langlands program

Numerical Jacquet--Langlands correspondence established in torsion setting

Insights into the structure of torsion in arithmetic groups

Abstract

We study torsion in the homology of arithmetic groups and give evidence that it plays a role in the Langlands program. We prove, among other results, a numerical form of a Jacquet--Langlands correspondence in the torsion setting.