Tohoku Mathematical Journal

On the finiteness of mod {$p$} Galois representations of a local field

Shinya Harada

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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 $K$.

Article information

Source
Tohoku Math. J. (2), Volume 59, Number 1 (2007), 67-77.

Dates
First available in Project Euclid: 16 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1176734748

Digital Object Identifier
doi:10.2748/tmj/1176734748

Mathematical Reviews number (MathSciNet)
MR2321993

Zentralblatt MATH identifier
1205.11059

Subjects
Primary: 11F80: Galois representations
Secondary: 11S15: Ramification and extension theory

Keywords
Galois representations local fields

Citation

Harada, Shinya. On the finiteness of mod {$p$} Galois representations of a local field. Tohoku Math. J. (2) 59 (2007), no. 1, 67--77. doi:10.2748/tmj/1176734748. https://projecteuclid.org/euclid.tmj/1176734748


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