Extensions of rank one (phi, Gamma)-modules and crystalline representations

TL;DR

This paper studies the structure of (phi, Gamma)-modules over unramified extensions of Q_p, focusing on their reducibility and crystalline lifts with specific Hodge-Tate weights, advancing understanding of p-adic Galois representations.

Contribution

It provides a parametrization of reducible two-dimensional (phi, Gamma)-modules over unramified extensions and characterizes those with crystalline lifts having particular Hodge-Tate weights.

Findings

Parametrization of reducible (phi, Gamma)-modules over unramified extensions.

Characterization of modules with crystalline lifts with specified Hodge-Tate weights.

Insights into the structure of reducible two-dimensional mod p Galois representations.

Abstract

Let K be a finite unramified extension of Q_p. We parametrize the (phi, Gamma)-modules corresponding to reducible two-dimensional mod p representations of G_K and characterize those which have reducible crystalline lifts with certain Hodge-Tate weights.