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.
Haution, O. (2017). On rational fixed points of finite group actions on the affine space. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 369(11), 8277-8290 [10.1090/tran/7184].
On rational fixed points of finite group actions on the affine space
Haution O.
2017
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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