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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Moduli of complexes on a proper morphism

Author: Max Lieblich
Journal: J. Algebraic Geom. 15 (2006), 175-206
Published electronically: September 7, 2005
MathSciNet review: 2177199
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Abstract | References | Additional Information

Abstract: Given a proper morphism $X\to S$, 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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Additional Information

Max Lieblich
Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
Address at time of publication: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000

Received by editor(s): February 21, 2005
Received by editor(s) in revised form: June 5, 2005
Published electronically: September 7, 2005
Additional Notes: Work on this paper was supported by a National Science Foundation Postdoctoral Fellowship.