Sur la cohomologie des compactifications de vari\'et\'es de Deligne-Lusztig
Haoran Wang

TL;DR
This paper investigates the étale cohomology of compactified Deligne-Lusztig varieties, providing new results for the general linear group and proposing conjectures for broader classes of reductive groups.
Contribution
It establishes a cohomological result for $GL_d$ compactifications and conjectures its extension to all reductive groups, advancing understanding of these varieties.
Findings
Proved a cohomology result for $GL_d$ compactifications.
Conjectured similar results for all reductive groups.
Enhanced understanding of the étale cohomology of Deligne-Lusztig compactifications.
Abstract
In this article, we study the \'etale cohomology of the compactification of Deligne-Lusztig varieties associated to a Coxeter element. We prove a result for the integral coefficients in the case of general linear group , and we conjecture that the similar result holds for general reductive groups.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry
