Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Hyunsuk Moon

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 7 (2014), 98-100.

First available in Project Euclid: 7 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F80: Galois representations
Secondary: 11G05: Elliptic curves over global fields [See also 14H52] 11N45: Asymptotic results on counting functions for algebraic and topological structures

Galois representations torsion points distribution


Moon, Hyunsuk. On the invariant $M(A_{/K}, n)$ of Chen-Kuan for Galois representations. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 7, 98--100. doi:10.3792/pjaa.90.98.

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