Finite group actions, rational fixed points and weak Néron models

Details Finite group actions, rational fixed points and weak Néron models Finite group actions, rational fixed points and weak Néron models

2010-09-07

arxiv.org/abs/1009.1281v3

Mathematics

Algebraic Geometry

Proposition 4.2 added and results in Section 4 generalized

Scientific paper

If $G$ is a finite $\ell$-group acting on an affine space $\mathbb{A}^n$ over a finite field $K$ of cardinality prime to $\ell$, Serre has shown that there exists a rational fixed point. We generalize this to the case where $K$ is a henselian discretely valued field of characteristic zero with algebraically closed residue field and with residue characteristic different from $\ell$. We also treat the case where the residue field is finite of cardinality $q$ such that $\ell$ divides $q-1$. To this aim, we study group actions on weak N\'eron models.

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