Lifting Galois representations over arbitrary number fields

TL;DR

This paper proves that under certain local conditions, every two-dimensional residual Galois representation over any number field can be lifted to a characteristic zero p-adic representation, advancing understanding of Galois deformation theory.

Contribution

It establishes a general lifting result for two-dimensional residual Galois representations over arbitrary number fields, extending previous work limited to specific fields.

Findings

Lifting is possible when local problems are unobstructed.

The result applies to all number fields, not just special cases.

Provides a framework for future research in Galois representations.

Abstract

It is proved that every two-dimensional residual Galois representation of the absolute Galois group of an arbitrary number field lifts to a characteristic zero $p$-adic representation, if local lifting problems at places above $p$ are unobstructed.