Finite group actions, rational fixed points and weak N\'eron models
Finite group actions, rational fixed points and weak N\'eron models
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有限群作用、有理不动点和弱 Neron 模型
DOI：
10.4310/pamq.2011.v7.n4.a7
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
J. Nicaise
中科院分区：
文献类型：
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作者：
H. Esnault;J. Nicaise
如果$G$是一个有限的$\ell$-群作用在一个有限域$K$上的仿射空间$\mathbb{A}^n$上，其基数与$\ell$互素，塞尔证明了存在一个有理不动点。我们推广到的情况下，其中$K$是一个亨氏离散值领域的特征零代数封闭的剩余领域和剩余的特点不同的$\ell$。我们还处理的情况下，剩余领域是有限的基数$q$，使$\ell$整除$q-1$。为此，我们研究弱Neron模型上的群作用。
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 Neron models.