On families of phi, Gamma-modules

• Main Authors: Kedlaya, Kiran S. (Contributor), Liu, Ruochuan (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Mathematical Sciences Publishers, 2012-08-08T15:11:24Z.
• Subjects: Article
• Online Access: Get fulltext

http://msp.berkeley.edu/ant/2010/4-7/p06.xhtml
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.