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2007 On the finiteness of mod {$p$} Galois representations of a local field
Shinya Harada
Tohoku Math. J. (2) 59(1): 67-77 (2007). DOI: 10.2748/tmj/1176734748

Abstract

Let $K$ be a local field and $k$ an algebraically closed field. We prove the finiteness of isomorphism classes of semisimple Galois representations of $K$ into $\GL_d(k)$ with bounded Artin conductor and residue degree. We calculate explicitly the number of totally ramified finite abelian extensions of $K$ with bounded conductor. Using this result, we give an upper bound for the number of certain Galois extensions of $K$.

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Shinya Harada. "On the finiteness of mod {$p$} Galois representations of a local field." Tohoku Math. J. (2) 59 (1) 67 - 77, 2007. https://doi.org/10.2748/tmj/1176734748

Information

Published: 2007
First available in Project Euclid: 16 April 2007

zbMATH: 1205.11059
MathSciNet: MR2321993
Digital Object Identifier: 10.2748/tmj/1176734748

Subjects:
Primary: 11F80
Secondary: 11S15

Rights: Copyright © 2007 Tohoku University

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