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

Xavier Caruso; David Lubicz

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arXiv · 1309.4194

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

Xavier Caruso·David Lubicz

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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 (\emph{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.

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Xavier Caruso, David Lubicz. 2013-09-17. Semi-simplified modulo $p$ of semi-stable representations: an algorithmic approach. https://arxiv.org/abs/1309.4194

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