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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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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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