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arXiv · 1009.1281

Finite group actions, rational fixed points and weak Néron models

Hélène Esnault·Johannes Nicaise
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Abstract

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 Néron models.

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Hélène Esnault, Johannes Nicaise. 2011-02-01. Finite group actions, rational fixed points and weak Néron models. https://arxiv.org/abs/1009.1281

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