Deformation conditions for pseudorepresentations

TL;DR

This paper extends deformation theory from Galois representations to pseudorepresentations, providing an axiomatic framework that ensures good deformation properties for pseudorepresentations with certain properties.

Contribution

It introduces an axiomatic approach to pseudorepresentations with specific properties, generalizing Ramakrishna's deformation theory to this broader context.

Findings

Pseudorepresentations with the property have a well-behaved deformation theory.

The theory generalizes Ramakrishna's results to pseudorepresentations.

Establishes foundational axioms for deformation of pseudorepresentations.

Abstract

Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur's Galois deformation theory for representations with that property. We introduce an axiomatic definition of pseudorepresentations with such a property. Among other things, we show that pseudorepresentations with a property enjoy a good deformation theory, generalizing Ramakrishna's theory to pseudorepresentations.