Finiteness Theorems for Deformations of Complexes

TL;DR

This paper establishes finiteness conditions for deformations of bounded complexes of modules over a profinite group, ensuring the existence of a strictly perfect complex representing the versal deformation over its deformation ring.

Contribution

It introduces new finiteness theorems that guarantee the representability of versal deformations by strictly perfect complexes in this setting.

Findings

Finiteness conditions for deformation representability

Existence of strictly perfect complexes over versal deformation rings

Conditions ensuring deformation functor is pro-representable

Abstract

We consider deformations of bounded complexes of modules for a profinite group G over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of G-modules that is strictly perfect over the associated versal deformation ring.