Tohoku Mathematical Journal

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

Shinya Harada

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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

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

First available in Project Euclid: 16 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Galois representations local fields


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.

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