Semi-simplified modulo p of semi-stable representations: an algorithmic approach

2013/09/17 by Caruso, Xavier, Lubicz, David
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1309.4194

Abstract

The aim of this paper is to present an algorithm the complexity of which is polynomial to compute the semi-simplified modulo p of a semi-stable \Q_p-representation of the absolute Galois group of a p-adic field (i.e. a finite extension of \Q_p). In order to do so, we use abundantly the p-adic Hodge theory and, in particular, the Breuil-Kisin modules theory.

Related

• Quasi-semi-stable representations
• Reduction modulo p of certain semi-stable representations
• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• Analyse p-adique et représentations Galoisiennes
• Polygones de Hodge, de Newton et de l'inertie modérée des représentations semi-stables