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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Algebroid prestacks and deformations of ringed spaces


Author: Wendy Lowen
Journal: Trans. Amer. Math. Soc. 360 (2008), 1631-1660
MSC (2000): Primary 13D10, 18F99
Published electronically: September 25, 2007
MathSciNet review: 2357708
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Abstract: For a ringed space $ (X,\mathcal{O})$, we show that the deformations of the abelian category $ \mathsf{Mod}(\mathcal{O})$ of sheaves of $ \mathcal{O}$-modules (Lowen and Van den Bergh, 2006) are obtained from algebroid prestacks, as introduced by Kontsevich. In case $ X$ is a quasi-compact separated scheme the same is true for $ \ensuremath{\mathsf{Qch}}(\mathcal{O})$, the category of quasi-coherent sheaves on $ X$. It follows in particular that there is a deformation equivalence between $ \mathsf{Mod}(\mathcal{O})$ and $ \mathsf{Qch}(\mathcal{O})$.


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Additional Information

Wendy Lowen
Affiliation: Departement DWIS, Vrije Universiteit Brussel, Pleinlaan 2,1050 Brussel, Belgium
Email: wlowen@vub.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04354-1
PII: S 0002-9947(07)04354-1
Received by editor(s): November 8, 2005
Received by editor(s) in revised form: May 15, 2006
Published electronically: September 25, 2007
Additional Notes: The author is a postdoctoral fellow FWO/CNRS. The author acknowledges the hospitality of the Institut de Mathématiques de Jussieu during her postdoctoral fellowship with CNRS
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.