On families of phi, Gamma-modules
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Kedlaya_On Families (arxiv).pdf
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289.41 KB
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Author(s)
Kedlaya, Kiran S.
Liu, Ruochuan
Alternative Title
On families of φ,Γ-modules
Date Issued
January 2011
Journal
Algebra & Number Theory
Publisher
Mathematical Sciences Publishers
Citation
Kedlaya, Kiran and Ruochuan Liu. "On families of φ,Γ-modules." Algebra & Number Theory 4.7 (2010): 943–967.
Version
Author's final manuscript
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.
Description
http://msp.berkeley.edu/ant/2010/4-7/p06.xhtml
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2140/ant.2010.4.943
