Haboush, W. J. A short proof of the Kempf vanishing theorem. (English) Zbl 0432.14027 Invent. Math. 56, 109-112 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 19 Documents MSC: 14L15 Group schemes 14M17 Homogeneous spaces and generalizations Keywords:Kempf vanishing theorem; generalized flag varieties; split semi-simple connected algebraic group; Borel subgroup; dominant line bundle; finite local group schemes; Steinberg representation PDFBibTeX XMLCite \textit{W. J. Haboush}, Invent. Math. 56, 109--112 (1980; Zbl 0432.14027) Full Text: DOI EuDML References: [1] Demazure, M.; Grothendieck, A., Séminaire de Géométrie Algébrique du Bois-Marie SGA 3 (196264), Berlin-Heidelberg-New York: Springer Verlag, Berlin-Heidelberg-New York · Zbl 0209.24201 [2] Cline, E., Parshall, B., Scott, L.: Cohomology, hyperalgebras, and representations, preprint · Zbl 0434.20024 [3] Haboush, W.; Malliavan, M. P., Central differential operators on semi-simple groups over fields of positive characteristic, Séminaire d’Algèbre. P. Dubreil, Proceedings, Paris (197879), Berlin, Heidelberg, New York: Springer Verlag, Berlin, Heidelberg, New York [4] Humphreys, J., On the hyperalgebra of semi-simple algebraic group, Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin, 203-210 (1970), New York: Academic Press, New York · Zbl 0367.20043 [5] Kempf, G.: Linear systems on homogeneous spaces, Ann. Math, 557-591 (1976) · Zbl 0327.14016 [6] Serre, J-P., Faisceaux algébriques cohérents, Ann Math., 61, 197-278 (1955) · Zbl 0067.16201 · doi:10.2307/1969915 [7] Steinberg, R., Representations of algebraic groups, Nagoya Math. J., 22, 33-56 (1963) · Zbl 0271.20019 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.