Large universal deformation rings

TL;DR

This paper presents examples of finite groups and mod p representations with large universal deformation rings, where the rings modulo p resemble a power series algebra, highlighting new phenomena in deformation theory.

Contribution

It introduces specific examples of representations with large universal deformation rings, expanding understanding of deformation rings in modular representation theory.

Findings

Universal deformation rings can be large, with mod p reductions isomorphic to power series algebras.

Examples demonstrate the existence of representations with stable endomorphisms given by scalars.

The structure of these deformation rings provides new insights into deformation theory of finite groups.

Abstract

We provide a series of examples of finite groups G and mod p representations V of G whose stable endomorphisms are all given by scalars such that V has a universal deformation ring R(G,V) which is large in the sense that R(G,V)/pR(G,V) is isomorphic to a power series algebra in one variable.