Semiregularity via derived deformation theory
arXiv:1112.6001
Abstract
We realise Buchweitz and Flenner's semiregularity map (and hence a fortiori Bloch's semiregularity map) as the tangent of a morphism of derived moduli functors. An immediate consequence is that it annihilates all obstructions (not just curvilinear ones) globally. This proves Bloch's semiregularity conjecture and establishes a global reduced obstruction theory.
Withdrawn - superseded by arXiv:1208.3111 (v3 contained errors in the formulae for the Goodwillie-Jones Chern character, and the key lemma, Prop 1.21, turns out to be Goodwillie's theorem on nilpotent ideals)