A reconstruction theorem for abelian categories of twisted sheaves

Abstract

We use an idea of Rosenberg to prove a reconstruction theorem for abelian categories of alpha-twisted quasi-coherent sheaves on quasi-compact and quasi-separated schemes X when alpha is in the Brauer group of X. By applying the work of Toën on derived Azumaya algebras, we give a proof of Căldăraru's conjecture.

arXiv comment14 pages; to appear in J. Reine Angew. Math.; previously entitled "Caldararu's conjecture on abelian categories of twisted sheaves"