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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
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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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Additional Information

Olivier Haution
Affiliation: Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstr. 39, D-80333 München, Germany
Email: olivier.haution@gmail.com

DOI: https://doi.org/10.1090/tran/7184
Keywords: Affine Cremona group, rational fixed points, finite group actions, fertile fields
Received by editor(s): September 14, 2016
Published electronically: May 1, 2017
Additional Notes: This work was supported by the DFG Grant HA 7702/1-1
Article copyright: © Copyright 2017 American Mathematical Society