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Die Quasiaffinität der Deligne-Lusztig-Varietäten. (The quasi- affinity of the Deligne-Lusztig varieties). (German) Zbl 0615.20021
Let G be a connected reductive algebraic group over the finite field with q elements. The socalled Deligne-Lusztig varieties in G/B, B a Borel subgroup, are known to be affine for q large by the work of P. Deligne and G. Lusztig [Ann. Math., II. Ser. 103, 103-161 (1976; Zbl 0336.20029)]. In this paper, the author proves that these varieties are always quasi-affine. This allows him then to generalize several of Deligne’s and Lusztig’s results including their vanishing theorem and statements about the eigenvalues of the Frobenius endomorphism of the non-vanishing cohomology group.
Reviewer: H.H.Andersen

MSC:
20G05 Representation theory for linear algebraic groups
20G40 Linear algebraic groups over finite fields
14L30 Group actions on varieties or schemes (quotients)
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