Former title: Deformations of residually reducible Galois representations via A-infinity algebra structure on Galois cohomology
Former title of working paper version: Cohomological control of deformation theory via A-infinity structure
Abstract: We introduce an A-infinity algebra structure on the Hochschild cohomology of the endomorphism bimodule of a finite-dimensional representation of an associative algebra. We prove that this structure determines a presentation for non-commutative deformations of the representation. From this, we deduce presentations of universal deformation rings of Galois representations. In turn, we apply these presentations in order to deduce universal deformation rings of Galois pseudorepresentations, supplying a a tangent and obstruction theory for pseudorepresentations. This generalizes the broadly used tangent and obstruction theory for Galois representations. We also give applications, calculating the ranks of certain Hecke algebras.
Back.