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A fixed point criterion for linear reductivity


Author: Peter Norman
Journal: Proc. Amer. Math. Soc. 50 (1975), 95-96
MSC: Primary 14L15; Secondary 20G15
DOI: https://doi.org/10.1090/S0002-9939-1975-0369377-5
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] J. Fogarty, Fixed point schemes, Amer. J. Math. 95 (1973). MR 0332805 (48:11130)
  • [2] J.-P. Serre, Groupes algébriques et corps de classes, Publ. Inst. Math. Univ. Nancago, VII, Actualités Sci. Indust., no. 1264, Hermann, Paris, 1959. MR 21 #1973; erratum, 30, p. 1200. MR 0103191 (21:1973)

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DOI: https://doi.org/10.1090/S0002-9939-1975-0369377-5
Article copyright: © Copyright 1975 American Mathematical Society

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