Obstructions for Deformations of Complexes

TL;DR

This paper introduces two methods for studying obstructions in deforming complexes of modules over profinite groups, advancing the understanding of their deformation theory in algebraic contexts.

Contribution

It presents two novel approaches to obstruction theory for deformations of complexes of modules over profinite groups, expanding the tools available in derived deformation theory.

Findings

Developed two new approaches to obstruction theory.

Applied methods to complexes over profinite groups.

Enhanced understanding of deformation obstructions.

Abstract

We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes $Z^\bullet$ of modules for a profinite group $G$ over a complete local Noetherian ring $A$ of positive residue characteristic $\ell$.