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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Uniqueness of enhancement for triangulated categories
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by Valery A. Lunts and Dmitri O. Orlov PDF
J. Amer. Math. Soc. 23 (2010), 853-908 Request permission

Abstract:

The paper contains general results on the uniqueness of a DG enhancement for triangulated categories. As a consequence we obtain such uniqueness for the unbounded derived categories of quasi-coherent sheaves, for the triangulated categories of perfect complexes, and for the bounded derived categories of coherent sheaves on quasi-projective schemes. If a scheme is projective, then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded derived categories of coherent sheaves. These results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product.
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Additional Information
  • Valery A. Lunts
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
  • MR Author ID: 265625
  • Email: vlunts@indiana.edu
  • Dmitri O. Orlov
  • Affiliation: Steklov Mathematical Institute, 8 Gubkina St., Moscow, Russia
  • Email: orlov@mi.ras.ru
  • Received by editor(s): September 5, 2009
  • Received by editor(s) in revised form: December 14, 2009
  • Published electronically: February 8, 2010
  • Additional Notes: The first author was partially supported by the NSA grant H98230-05-1-0050
    The second author was partially supported by grant RFFI 08-01-00297 and grant NSh-1987.2008.1
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 23 (2010), 853-908
  • MSC (2010): Primary 14F05, 18E30
  • DOI: https://doi.org/10.1090/S0894-0347-10-00664-8
  • MathSciNet review: 2629991