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Mod $p$ Galois representations of solvable image

Authors: Hyunsuk Moon and Yuichiro Taguchi
Journal: Proc. Amer. Math. Soc. 129 (2001), 2529-2534
MSC (2000): Primary 11R29, 11R32
Published electronically: January 23, 2001
MathSciNet review: 1838373
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It is proved that, for a number field $K$ and a prime number $p$, there exist only finitely many isomorphism classes of continuous semisimple Galois representations of $K$ into $\operatorname{GL}_{d}(\overline{\mathbb{F}}_{p})$ of fixed dimension $d$ and bounded Artin conductor outside $p$ which have solvable images. Some auxiliary results are also proved.

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Additional Information

Hyunsuk Moon
Affiliation: Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan
Address at time of publication: Department of Mathematics, College of Natural Sciences, Seoul National University, Seoul, 151-742, Korea

Yuichiro Taguchi
Affiliation: Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

Received by editor(s): January 12, 2000
Published electronically: January 23, 2001
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2001 American Mathematical Society