The cohomology of Deligne–Lusztig varieties for the general linear group

  • Sascha Orlik


We propose two inductive approaches for determining the cohomology of Deligne–Lusztig varieties in the case of \(G={{\mathrm{GL}}}_n\). The first one uses Demazure compactifications and analyzes the corresponding Mayer–Vietoris spectral sequence. This allows us to give an inductive formula for the Tate twist \(-1\) contribution of the cohomology of a DL-variety. The second approach relies on considering more generally DL-varieties attached to hypersquares in the Weyl group. Here we give explicit formulas for the cohomology of height-one elements.



I want to thank Olivier Dudas for his numerous remarks on this paper. I am grateful for the invitation to Paris and all the discussions with François Digne and Jean Michel. Finally I thank Roland Huber, Michael Rapoport and Markus Reineke for their support. Dedicated to Michael Rapoport on the occasion of his 65th birthday.


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Authors and Affiliations

  1. 1.Fachbereich C - Mathematik und NaturwissenschaftenBergische Universität WuppertalWuppertalGermany

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