On families of phi, Gamma-modules
Author(s)Kedlaya, Kiran S.; Liu, Ruochuan
On families of φ,Γ-modules
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Algebra & Number Theory
Mathematical Sciences Publishers
Kedlaya, Kiran and Ruochuan Liu. "On families of φ,Γ-modules." Algebra & Number Theory 4.7 (2010): 943–967.
Author's final manuscript