Haastert, Burkhard Die Quasiaffinität der Deligne-Lusztig-Varietäten. (The quasi- affinity of the Deligne-Lusztig varieties). (German) Zbl 0615.20021 J. Algebra 102, 186-193 (1986). 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 Cited in 7 Documents MSC: 20G05 Representation theory for linear algebraic groups 20G40 Linear algebraic groups over finite fields 14L30 Group actions on varieties or schemes (quotients) Keywords:connected reductive algebraic group; Deligne-Lusztig varieties; Borel subgroup; quasi-affine; vanishing theorem; eigenvalues of the Frobenius endomorphism PDF BibTeX XML Cite \textit{B. Haastert}, J. Algebra 102, 186--193 (1986; Zbl 0615.20021) Full Text: DOI References: [1] Demazure, M, Désingularisation des variétés de Schubert généralisées, Annales scientifiques de l’ENS, tome 7, 53-88, (1974) · Zbl 0312.14009 [2] deligne, P; Lusztig, G, Representations of reductive groups over finite fields, Ann. of math., 103, 103-161, (1976) · Zbl 0336.20029 [3] Digne, F; Michel, J, Descente de shintani des caractéres d’un groupe de Chevalley fini, C. R. acad. sci. Paris ser. A, 291, 571-574, (1980) · Zbl 0456.20021 [4] \scF. Digne und J. Michel, Fonctions L des variétés de Deligne-Lusztig et Descente de Shintani, in Vorbereitung. · Zbl 0608.20027 [5] Grothendieck, A; Dieudonne, J, Elements de Géométrie algébrique; étude globale élémentaire de quelques classes de morphismes, Publ. math. IHES, Vol. 8, (1961) [6] Hochschild, G, Basic theory of algebraic groups and Lie algebras, () · Zbl 0229.20042 [7] Lusztig, G, Representations of finite Chevalley groups, () · Zbl 0372.20033 [8] Lusztig, G, Characters of reductive groups over a finite field, () · Zbl 0930.20041 [9] Milne, J.S, Étale cohomology, (1980), Princeton Univ. Press London · Zbl 0433.14012 [10] Steinberg, R, Conjugacy classes in algebraic groups, () · Zbl 0192.36202 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.