Extended deformation functors

Details Extended deformation functors Extended deformation functors

1999-10-14

arxiv.org/abs/math/9910071v2

Internat. Math. Res. Notices 14 (2002) 719-756.

Mathematics

Algebraic Geometry

Contains the previously announced part II

Scientific paper

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.

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