Title: Deformation conditions for 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.