Local Indecomposability of Hilbert Modular Galois Representations

TL;DR

This paper proves that certain Galois representations associated with non-CM nearly p-ordinary Hilbert modular forms are indecomposable when restricted to the p-decomposition group, under mild assumptions.

Contribution

It establishes the local indecomposability of Galois representations for a broad class of Hilbert modular forms, extending previous results.

Findings

Galois representations are indecomposable under specified conditions.

Results apply to non-CM nearly p-ordinary weight two Hilbert modular forms.

Provides new insights into the local structure of Galois representations.

Abstract

We prove the indecomposability of Galois representation restricted to the p-decomposition group attached to a non CM nearly p-ordinary weight two Hilbert modular form under mild conditions.