On a relation of overconvergence and $F$-analyticity on $p$-adic Galois representations of a $p$-adic field $F

Let $p$ be a prime number. There are properties called ``overconvergence'' and ``$F$-analyticity'' for $p$-adic Galois representations of a $p$-adic field $F$. By Berger's work, it is known that $F$-analyticity is stricter than overconvergence. In this article, we show that,...

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Bibliographic Details
Main Author Takata, Megumi
Format Journal Article
LanguageEnglish
Published 14.09.2019
Subjects
Mathematics - Number Theory
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Summary:Let $p$ be a prime number. There are properties called ``overconvergence'' and ``$F$-analyticity'' for $p$-adic Galois representations of a $p$-adic field $F$. By Berger's work, it is known that $F$-analyticity is stricter than overconvergence. In this article, we show that, in many cases, an overconvergent Galois representation is $F$-analytic up to a twist by a character. This result emphasizes the necessity of the theory of $(\varphi,\Gamma)$-modules over the multivariable Robba ring, by which we expect to study all $p$-adic Galois representations.
DOI:10.48550/arxiv.1909.06725