Open Access
July 2014 On the invariant $M(A_{/K}, n)$ of Chen-Kuan for Galois representations
Hyunsuk Moon
Proc. Japan Acad. Ser. A Math. Sci. 90(7): 98-100 (July 2014). DOI: 10.3792/pjaa.90.98


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.


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Hyunsuk Moon. "On the invariant $M(A_{/K}, n)$ of Chen-Kuan for Galois representations." Proc. Japan Acad. Ser. A Math. Sci. 90 (7) 98 - 100, July 2014.


Published: July 2014
First available in Project Euclid: 7 August 2014

zbMATH: 1310.11063
MathSciNet: MR3249832
Digital Object Identifier: 10.3792/pjaa.90.98

Primary: 11F80
Secondary: 11G05 , 11N45

Keywords: distribution , Galois representations , torsion points

Rights: Copyright © 2014 The Japan Academy

Vol.90 • No. 7 • July 2014
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