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arXiv · 2403.00979

Geometry and cohomology of compactified Deligne--Lusztig varieties

Yingying Wang
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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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Yingying Wang. 2024-03-01. Geometry and cohomology of compactified Deligne--Lusztig varieties. https://doi.org/10.1093/imrn%2Frnaf099

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