On rational fixed points of finite group actions on the affine space

Haution, Olivier

doi:10.1090/tran/7184

On rational fixed points of finite group actions on the affine space
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Trans. Amer. Math. Soc. 369 (2017), 8277-8290 Request permission

Abstract:

Consider a finite $l$-group acting on the affine space of dimension $n$ over a field $k$, whose characteristic differs from $l$. We prove the existence of a fixed point, rational over $k$, in the following cases:

— The field $k$ is $p$-special for some prime $p$ different from its characteristic.

— The field $k$ is perfect and fertile, and $n = 3$.

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