Quotient of Deligne-Lusztig varieties

TL;DR

This paper investigates the quotient of certain Deligne-Lusztig varieties by a unipotent group and demonstrates that, in specific cases, their cohomology relates to smaller varieties associated with Levi subgroups.

Contribution

It introduces a method to relate the cohomology of quotients of parabolic Deligne-Lusztig varieties to those of smaller varieties linked to Levi subgroups.

Findings

Cohomology of quotients can be expressed via smaller parabolic varieties

Results apply to particular cases with Levi subgroups

Provides new insights into the structure of Deligne-Lusztig varieties

Abstract

We study the quotient of parabolic Deligne-Lusztig varieties by a finite unipotent group U^F where U is the unipotent radical of a rational parabolic subgroup P = L U. We show that in some particular cases the cohomology of this quotient can be expressed in terms of "smaller" parabolic Deligne-Lusztig varieties associated to the Levi subgroup L.