Moduli of complexes on a proper morphism

Details Moduli of complexes on a proper morphism Moduli of complexes on a proper morphism

2005-02-09

arxiv.org/abs/math/0502198v2

Mathematics

Algebraic Geometry

25 pages. Revised version, to appear in the Journal of Algebraic Geometry

Scientific paper

Given a proper morphism X -> S, we show that a large class of objects in the derived category of X naturally form an Artin stack locally of finite presentation over S. This class includes S-flat coherent sheaves and, more generally, contains the collection of all S-flat objects which can appear in the heart of a reasonable sheaf of t-structures on X. In this sense, this is the Mother of all Moduli Spaces (of sheaves). The proof proceeds by studying the finite presentation properties, deformation theory, and Grothendieck existence theorem for objects in the derived category, and then applying Artin's representability theorem.

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