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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A fixed point criterion for linear reductivity

Author: Peter Norman
Journal: Proc. Amer. Math. Soc. 50 (1975), 95-96
MSC: Primary 14L15; Secondary 20G15
MathSciNet review: 0369377
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Abstract: Let $ G$ be a linear algebraic group over an algebraically closed field. If for all actions of $ G$ on smooth schemes, the fixed point scheme is smooth, then $ G$ is linearly reductive under either of the additional assumptions: (a) the ground field is characteristic zero, or (b) $ G$ is connected, reduced, and solvable.

References [Enhancements On Off] (What's this?)

  • [1] John Fogarty, Fixed point schemes, Amer. J. Math. 95 (1973), 35–51. MR 0332805
  • [2] Jean-Pierre Serre, Groupes algébriques et corps de classes, Publications de l’institut de mathématique de l’université de Nancago, VII. Hermann, Paris, 1959 (French). MR 0103191

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Article copyright: © Copyright 1975 American Mathematical Society