Extended deformation functors

Abstract

We introduce a precise notion, in terms of few Schlessinger's type conditions, of extended deformation functors which is compatible with most of recent ideas in the Derived Deformation Theory (DDT) program and with geometric examples. With this notion we develop the (extended) analogue of Schlessinger and obstruction theories. The inverse mapping theorem holds for natural transformations of extended deformation functors and all such functors with finite dimensional tangent space are prorepresentable in the homotopy category.

Contains the previously announced part II

References in corpus (3)

• Deformation quantization of Poisson manifolds, I
• Introduction to sh Lie algebras for physicists
• DG coalgebras as formal stacks

Cited by in corpus (7)

• Semicosimplicial DGLAs in deformation theory
• Semiregularity and obstructions of complete intersections
• Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
• Cocommutative coalgebras: homotopy theory and Koszul duality
• Deformations of algebraic schemes via Reedy-Palamodov cofibrant resolutions
• Endomorphisms of Koszul complexes: formality and application to deformation theory
• Hypersurfaces and generalized deformations