1999/10/31 by Marco Manetti
Mathematics · #math.AG #math.AC #math.QA #msc:13D10 #msc:14B10 #msc:14D15
published as Internat. Math. Res. Notices 14 (2002) 719-756. · Contains the previously announced part II
arxiv created 2001/03/16 · arxiv updated 2009/11/30
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.