Quasi-semi-stable representations

Xavier Caruso; Tong Liu

Bulletin de la Société Mathématique de France (2009)

  • Volume: 137, Issue: 2, page 185-223
  • ISSN: 0037-9484

Abstract

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Fix K a p -adic field and denote by G K its absolute Galois group. Let K ∞ be the extension of K obtained by adding p n -th roots of a fixed uniformizer, and G ∞ ⊂ G K its absolute Galois group. In this article, we define a class of p -adic torsion representations of G ∞ , 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 of two lattices in a crystalline (resp. semi-stable) Galois representation.

How to cite

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Caruso, Xavier, and Liu, Tong. "Quasi-semi-stable representations." Bulletin de la Société Mathématique de France 137.2 (2009): 185-223. <http://eudml.org/doc/272378>.

@article{Caruso2009,
abstract = {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 of two lattices in a crystalline (resp. semi-stable) Galois representation.},
author = {Caruso, Xavier, Liu, Tong},
journal = {Bulletin de la Société Mathématique de France},
keywords = {torsion Galois representations; semi-stable representations; norm field theory},
language = {eng},
number = {2},
pages = {185-223},
publisher = {Société mathématique de France},
title = {Quasi-semi-stable representations},
url = {http://eudml.org/doc/272378},
volume = {137},
year = {2009},
}

TY - JOUR
AU - Caruso, Xavier
AU - Liu, Tong
TI - Quasi-semi-stable representations
JO - Bulletin de la Société Mathématique de France
PY - 2009
PB - Société mathématique de France
VL - 137
IS - 2
SP - 185
EP - 223
AB - 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 of two lattices in a crystalline (resp. semi-stable) Galois representation.
LA - eng
KW - torsion Galois representations; semi-stable representations; norm field theory
UR - http://eudml.org/doc/272378
ER -

References

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  12. [12] —, « Moduli of finite flat group schemes and modularity », to appear in Ann. of Math. Zbl1201.14034
  13. [13] T. Liu – « Torsion p -adic Galois representation and a conjecture by Fontaine », Ann. Sci. École Norm. Sup.40 (2007), p. 633–674. Zbl1163.11043MR2191528
  14. [14] —, « On lattices in semi-stable representations: a proof of a conjecture of Breuil », Compos. Math.144 (2008), p. 61–88. Zbl1133.14020MR2388556
  15. [15] M. Raynaud – « Schémas en groupes de type ( p , ⋯ , p ) », Bull. Soc. Math. France102 (1974), p. 241–280. Zbl0325.14020MR419467
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