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Representability of derived stacks

Published online by Cambridge University Press:  31 January 2012

J.P. Pridham
J.P. Pridham*
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 [email protected]
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Abstract

Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify for many applications. Provided a derived analogue of Schlessinger's condition holds, the theorem reduces to verifying conditions on the underived part and on cohomology groups. Another simplification is that functors need only be defined on nilpotent extensions of discrete rings. Finally, there is a pre-representability theorem, which can be applied to associate explicit geometric stacks to dg-manifolds and related objects.

Keywords

Representabilityderived moduli
Type
Research Article
Information
Journal of K-Theory , Volume 10 , Issue 2 , October 2012 , pp. 413 - 453
Copyright
Copyright © ISOPP 2011

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