Algebra & Number Theory
- Algebra Number Theory
- Volume 4, Number 7 (2010), 943-967.
On families of $\varphi,\Gamma$-modules
Berger and Colmez (2008) formulated a theory of families of overconvergent étale -modules associated to families of -adic Galois representations over -adic Banach algebras. In contrast with the classical theory of -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 -modules can locally be converted into a family of -adic representations in a unique manner, providing the “local” equivalence. There is a global mod obstruction related to the moduli of residual representations.
Algebra Number Theory, Volume 4, Number 7 (2010), 943-967.
Received: 10 December 2009
Accepted: 10 January 2010
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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