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2010 On families of $\varphi,\Gamma$-modules
Kiran Kedlaya, Ruochuan Liu
Algebra Number Theory 4(7): 943-967 (2010). DOI: 10.2140/ant.2010.4.943

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.

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Kiran Kedlaya. Ruochuan Liu. "On families of $\varphi,\Gamma$-modules." Algebra Number Theory 4 (7) 943 - 967, 2010. https://doi.org/10.2140/ant.2010.4.943

Information

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

zbMATH: 1278.11060
MathSciNet: MR2776879
Digital Object Identifier: 10.2140/ant.2010.4.943

Subjects:
Primary: 11F80
Secondary: 11S20

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

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.4 • No. 7 • 2010
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