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

Author: Olivier Haution
Journal: Trans. Amer. Math. Soc. 369 (2017), 8277-8290
MSC (2010): Primary 14G05, 14L30, 14C25, 14F30
DOI: https://doi.org/10.1090/tran/7184
Published electronically: May 1, 2017
MathSciNet review: 3695861
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Abstract: Consider a finite -group acting on the affine space of dimension over a field , whose characteristic differs from . We prove the existence of a fixed point, rational over , in the following cases:

-- The field is -special for some prime different from its characteristic.

-- The field is perfect and fertile, and .

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