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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, Lecture Notes in math. Berlin-Heidelberg-New York: Springer Verlag 1962/64
[2] Cline, E., Parshall, B., Scott, L.: Cohomology, hyperalgebras, and representations, preprint
[3] Haboush, W.: Central differential operators on semi-simple groups over fields of positive characteristic. In: Séminaire d’Algèbre. P. Dubreil, Proceedings, Paris (M.P. Malliavan, ed.) Lecture Notes in Math. Berlin, Heidelberg, New York: Springer Verlag 1978/79 · Zbl 0432.14029
[4] Humphreys, J.: On the hyperalgebra of semi-simple algebraic group, In: Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin, pp. 203–210. New York: Academic Press 1970
[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
[7] Steinberg, R.: Representations of algebraic groups, Nagoya Math. J.22, 33–56 (1963) · Zbl 0271.20019
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