A fixed point criterion for linear reductivity
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- by Peter Norman PDF
- Proc. Amer. Math. Soc. 50 (1975), 95-96 Request permission
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
- John Fogarty, Fixed point schemes, Amer. J. Math. 95 (1973), 35–51. MR 332805, DOI 10.2307/2373642
- 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
Additional Information
- © Copyright 1975 American Mathematical Society
- 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