On the generic part of the cohomology of Shimura varieties of abelian type

TL;DR

This paper proves a torsion vanishing result for the generic part of the cohomology of Shimura varieties of abelian type, confirming a conjecture and using novel methods that avoid trace formula techniques.

Contribution

It introduces a new proof of torsion vanishing for Shimura varieties of abelian type using the unipotent categorical local Langlands correspondence, bypassing endoscopic classification.

Findings

Proves torsion vanishing for the generic cohomology of Shimura varieties of abelian type.

Confirms a conjecture by Hamann--Lee.

Employs novel methods avoiding trace formula techniques.

Abstract

This article contributes to the study of the generic part of the cohomology of Shimura varieties. Under a mild restriction of the characteristic of the coefficient field, we prove a torsion vanishing result for Shimura varieties of abelian type, confirming a conjecture by Hamann--Lee. Our proofs utilize the unipotent categorical local Langlands correspondence and, in contrast to previous works, do not rely on the endoscopic classification of representations or on other results established through trace formula techniques.