2018/09/07 by Carl Wang-Erickson, Wang-Erickson, Carl · 3 citations
Mathematics · #11F80 #14A22 (primary) #14D15 #16E45 (secondary) #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Associative property #Bimodule #Cohomology #Commutative property #Deformation theory #Endomorphism #FOS: Mathematics #Fundamental theorem of Galois theory #Galois cohomology #Galois group #Homotopy and Cohomology in Algebraic Topology #Indecomposable module #Mathematics #Number Theory (math.NT) #Order (exchange) #Pure mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AG #math.NT #math.RA #math.RT #msc:11F80 #msc:14A22 #msc:14D15 #msc:16E45
paper · pdf · doi:10.48550/arxiv.1809.02484
published in arXiv (Cornell University) (Cornell University) · 84 pages, major revisions
openalex publication_date 2018/09/07 · arxiv created 2020/04/03 · arxiv updated 2020/04/07 · openalex created_date 2020/04/10 · openalex updated_date 2026/07/28
We introduce an A_∞-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.