Die Quasiaffinität der Deligne-Lusztig-Varietäten. (The quasi- affinity of the Deligne-Lusztig varieties)
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 \textit{P. Deligne} and \textit{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.
eigenvalues of the Frobenius endomorphism
scientific article; zbMATH DE number 3995966
scientific article