Automorphy lifting with adequate image

TL;DR

This paper extends automorphy lifting theorems for Galois representations over CM fields by weakening the big image condition, broadening the scope of automorphy results in number theory.

Contribution

It generalizes existing automorphy lifting theorems to include cases with less restrictive residual image assumptions over CM fields.

Findings

Broadened automorphy lifting criteria for Galois representations.

Relaxed residual image conditions enable new automorphy applications.

Enhanced understanding of automorphy in CM number fields.

Abstract

Let $F$ be a CM number field. We generalize existing automorphy lifting theorems for regular residually irreducible $p$-adic Galois representations over $F$ by relaxing the big image assumption on the residual representation.