Obstructions to Deformations of DG Modules

Original · EN

Let k be a field and n > 0. There exists a DG k-module (V,d) and various approximations d + t d₁ + t² d₂ +... + tⁿ dₙ to a differential on V[[t]], one of which is a non-trivial deformation, another is obstructed, and another is unobstructed at order n. The analogous problem in the category of k-algebras in characteristic zero remains a long-standing open question.