Families of p-adic Galois representations and (phi,Gamma)-modules

TL;DR

This paper explores the connection between p-adic Galois representations and overconvergent (phi,Gamma)-modules, constructing a natural open subspace where these modules are induced by Galois representations, advancing understanding in p-adic Hodge theory.

Contribution

It introduces a natural open subspace of (phi,Gamma)-modules where they are induced by Galois representations, providing new insights into their relationship.

Findings

Construction of a natural open subspace of (phi,Gamma)-modules

Establishment of the link between this subspace and Galois representations

Enhanced understanding of p-adic Hodge theoretic structures

Abstract

We investigate the relation between p-adic Galois representations and overconvergent (phi,Gamma)-modules in families. Especially we construct a natural open subspace of a family of (phi,Gamma)-modules, over which it is induced by a family of Galois-representations.