Geometry and cohomology of compactified Deligne--Lusztig varieties

Abstract

For connected reductive groups together with a Frobenius root $F$, we show that the cohomology of the structure sheaf and respectively the canonical sheaf for compactified Deligne--Lusztig varieties associated to an element in the free monoid generated by the simple reflections is isomorphic to that of a minimal length element in an $F$-conjugacy class in the Weyl group.

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References in corpus (2)

• Grothendieck Duality for Deligne-Mumford Stacks
• Cohomology and geometry of Deligne--Lusztig varieties for ${\mathrm{GL}}_n$