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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Algebroid prestacks and deformations of ringed spaces
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by Wendy Lowen PDF
Trans. Amer. Math. Soc. 360 (2008), 1631-1660 Request permission

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 $\mathsf {Qch}(\mathcal {O})$.
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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