Obstruction Theory for Objects in Abelian and Derived Categories

2005/08/01 by Wendy Lowen · 6 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Geometric and Algebraic Topology

paper · doi:10.1081/agb-200066155

Abstract

ABSTRACT In this article, we develop the obstruction theory for lifting complexes, up to quasi-isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a particular case we also obtain the corresponding obstruction theory for lifting of objects in terms of Yoneda Ext-groups. In an appendix we prove the existence of miniversal derived deformations of complexes.

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• Deformation of exceptional collections
• Abelian and derived deformations in the presence of Z-generating geometric helices
• Infinitesimal Derived Torelli Theorem for K3 surfaces
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Related

• Obstruction theory for objects in abelian and derived categories
• Deformation theory for a morphism in the derived category with fixed lift of the codomain
• Deformation theory of abelian categories
• Notes on formal deformations of abelian categories
• Deformation theory from the point of view of fibered categories