Equations differentielles p-adiques et (phi,N)-modules filtres

By Laurent Berger. 2004

65 citations recorded by the source corpus.

The goal of this article is to show that the following two categories are equivalent (1) the category of filtered (phi,N,G_K)-modules (2) the category of (phi,Gamma_K)-modules over the Robba ring such that the Lie algebra of Gamma_K acts locally trivially. Furthermore, we show that under this equivalence, the admissible filtered (phi,N,G_K)-modules correspond to the etale (phi,Gamma_K)-modules, which gives a new proof of Colmez-Fontaine's theorem.

View Paper: https://www.semanticscholar.org/paper/0ef2d8b88a4b95121cbf7c3dfbc736ac5415e436

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Citations in the corpus

On period spaces for p-divisible groups (2007, unknown): “On the other hand Berger’s proof [1] of the Colmez-Fontaine Theorem shows that this inclusion induces a bijection on rigid analytic points (with K/K0 finite), or more generally points of F an wa with with values in a discretely valued field K.”
Construction de (φ,Γ)-modules: représentations p-adiques et B-paires (2008, background): “Si D est un (ϕ, N )-module filtré, on note M(D) le (ϕ, 0K )-module construit dans [Berger 2004a, §II.2].”
Relative P-adic Hodge Theory: Foundations (2013, unknown): “63 3.6 The perfectoid correspondence for Banach algebras . . . . . . . . . . . . . . 67”
Period spaces for Hodge structures in equal characteristic (2005, methodology): “Meanwhile there are many more ways to prove this conjecture [17, 6, 42].”
Slope filtrations for relative Frobenius (2006, background): “Thanks to Laurent Berger for the original suggestion to con sider relative Frobenius and for subsequent discussions, to Lucia di Vizio for providing the reference to Praagman's work, and to Peter Schneider for additional comments.”