Geometry and cohomology of compactified Deligne--Lusztig varieties

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Abstract

For connected reductive groups, we prove that the cohomology of the structure sheaf and the canonical sheaf for compactified Deligne--Lusztig varieties associated to a tuple (w₁, , wᵣ) of Weyl group elements depends only on the F-support of (w₁, , wᵣ).

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