Coxeter orbits and Brauer trees II

TL;DR

This paper investigates the assumptions related to torsion in the modular l-adic cohomology of Deligne-Lusztig varieties linked to Coxeter elements, confirming their validity for most group types.

Contribution

It proves the assumptions (W) and (S) hold for all groups except types E_7 and E_8, clarifying the behavior of torsion in these cohomologies.

Findings

Assumptions (W) and (S) are valid for all group types except E_7 and E_8.

The paper advances understanding of torsion phenomena in modular cohomology of Deligne-Lusztig varieties.

Provides partial validation of conjectures about cohomological torsion in algebraic groups.

Abstract

The purpose of this paper is to discuss the validity of the assumptions (W) and (S) stated in a previous work, about the torsion in the modular l-adic cohomology of Deligne-Lusztig varieties associated to Coxeter elements. We prove that both (W) and (S) hold except for groups of type E_7 or E_8.