Algebra & Number Theory

On families of $\varphi,\Gamma$-modules

Kiran Kedlaya and Ruochuan Liu

Full-text: Open access

Abstract

Berger and Colmez (2008) formulated a theory of families of overconvergent étale (φ,Γ)-modules associated to families of p-adic Galois representations over p-adic Banach algebras. In contrast with the classical theory of (φ,Γ)-modules, the functor they obtain is not an equivalence of categories. In this paper, we prove that when the base is an affinoid space, every family of (overconvergent) étale (φ,Γ)-modules can locally be converted into a family of p-adic representations in a unique manner, providing the “local” equivalence. There is a global mod p obstruction related to the moduli of residual representations.

Article information

Source
Algebra Number Theory, Volume 4, Number 7 (2010), 943-967.

Dates
Received: 10 December 2009
Accepted: 10 January 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729590

Digital Object Identifier
doi:10.2140/ant.2010.4.943

Mathematical Reviews number (MathSciNet)
MR2776879

Zentralblatt MATH identifier
1278.11060

Subjects
Primary: 11F80: Galois representations
Secondary: 11S20: Galois theory

Keywords
$p$-adic Galois representations $(\varphi,\Gamma)$-modules

Citation

Kedlaya, Kiran; Liu, Ruochuan. On families of $\varphi,\Gamma$-modules. Algebra Number Theory 4 (2010), no. 7, 943--967. doi:10.2140/ant.2010.4.943. https://projecteuclid.org/euclid.ant/1513729590


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