Semiregularity via derived deformation theory

TL;DR

This paper proves Bloch's semiregularity conjecture by representing semiregularity maps as tangent maps of derived moduli functors, leading to a global reduced obstruction theory that annihilates all obstructions.

Contribution

It provides a derived deformation theory framework to realize semiregularity maps as tangent maps, proving Bloch's conjecture and establishing a global obstruction theory.

Findings

Proves Bloch's semiregularity conjecture.

Realizes semiregularity maps as tangent maps of derived functors.

Establishes a global reduced obstruction theory.

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.