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A short proof of the Kempf vanishing theorem. (English) Zbl 0432.14027


MSC:

14L15 Group schemes
14M17 Homogeneous spaces and generalizations
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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
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