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11-XX Number theory
11Fxx Discontinuous groups and automorphic forms
11F85 $p$ -adic theory, local fields

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Quasi-semi-stable representations

Xavier Caruso, Tong Liu (2009)

Bulletin de la Société Mathématique de France

Fix $K$ a $p$ -adic field and denote by $G_{K}$ its absolute Galois group. Let $K_{\infty}$ be the extension of $K$ obtained by adding $p^{n}$ -th roots of a fixed uniformizer, and $G_{\infty} \subset G_{K}$ its absolute Galois group. In this article, we define a class of $p$ -adic torsion representations of $G_{\infty}$ , calledquasi-semi-stable. We prove that these representations are “explicitly” described by a certain category of linear algebraic objects. The results of this note should be considered as a first step in the understanding of the structure of quotient...

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