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Cohomological dimension of group schemes

Published online by Cambridge University Press:  22 January 2016

Hiroshi Umemura
Hiroshi Umemura*
Affiliation:
Department of Mathematics, Nagoya University
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In Umemura [9], we calculated the invariants algcd (G), p(G), q(G) for a commutative algebraic group G. We remark that all the results hold for a group scheme which is not necessarily commutative.

To determine p(G), I cannot succeed in dropping the hypothesis “quasi-projective” but this assumption is satisfied in the characteristic 0 case.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 52 , December 1973 , pp. 47 - 52
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Andreotti, A. and Grauert, H.: Théorème de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 90 (1962), 193–259.CrossRefGoogle Scholar
[2] Chow, W. L.: On the projective embedding of homogeneous varieties. A symp. in honor of S. Lefschetz, 122–128, Princeton University press.Google Scholar
[3] Dieudonné, J. et Grothendieck, A.: E.G.A.Google Scholar
[4] Hartshorne, R.: Ample subvarieties of algebraic varieties, Lecture notes in mathematics 156, Springer.Google Scholar
[5] Matsushima, Y.: Fibres holomorphes sur un tore complexe, Nagoya Math. J., 14, 1–24 (1959).CrossRefGoogle Scholar
[6] Mumford, D.: Abelian varieties, Oxford University press.Google Scholar
[7] Oort, F.: Algebraic group schemes in characteristic zero are reduced, Inventiones math., 2 (1966), 79–80.CrossRefGoogle Scholar
[8] Rosenlicht, M.: Some basic theorems on algebraic groups, Amer. J. of Math., 78 (1956), 401–443.CrossRefGoogle Scholar
[9] Umemura, H.: Dimension cohomologique des groupes algébriques commutatif s, Ann, Scien. de l’Ecole Normale Supérieure, 4e series 5 (1972), 265–276.Google Scholar
[10] Umemura, H.: La dimension cohomologique des surfaces algébriques, Nagoya Math. J., 47 (1972), 155–160.CrossRefGoogle Scholar