Algebroid prestacks and deformations of ringed spaces
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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 $\mathsf {Qch}(\mathcal {O})$, the category of quasi-coherent sheaves on $X$. It follows in particular that there is a deformation equivalence between $\mathsf {Mod}(\mathcal {O})$ and $\mathsf {Qch}(\mathcal {O})$.References
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Additional Information
- Wendy Lowen
- Affiliation: Departement DWIS, Vrije Universiteit Brussel, Pleinlaan 2,1050 Brussel, Belgium
- Email: wlowen@vub.ac.be
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 1631-1660
- MSC (2000): Primary 13D10, 18F99
- DOI: https://doi.org/10.1090/S0002-9947-07-04354-1
- MathSciNet review: 2357708