On the invariant $M(A_{/K}, n)$ of Chen-Kuan for Galois representations

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Hyunsuk Moon¹ 

[1] Department of Mathematics, College of Natural Sciences, Kyungpook National University

关键词: Galois representations;    torsion points;    distribution.;   

DOI  :  10.3792/pjaa.90.98

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

Let $X$ be a finite set with a continuous action of the absolute Galois group of a global field $K$. We suppose that $X$ is unramified outside a finite set $S$ of places of $K$. For a place $\mathfrak{p} \notin S$, let $N_{X, \mathfrak{p}}$ be the number of fixed points of $X$ by the Frobenius element $\mathrm{Frob}_{\mathfrak{p}} \subset G_{K}$. We define the average value $M(X)$ of $N_{X, \mathfrak{p}}$ where $\mathfrak{p}$ runs through the non-archimedean places in $K$. This generalize the invariant of Chen-Kuan and we apply this for Galois representations. Our results show that there is a certain relationship between $M(X)$ and the size of the image of Galois representations.

【 授权许可】

Unknown