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

 

Twisting derived equivalences


Author: Oren Ben-Bassat
Journal: Trans. Amer. Math. Soc. 361 (2009), 5469-5504
MSC (2000): Primary 14D22, 14K99, 18E30
Published electronically: April 21, 2009
MathSciNet review: 2515820
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Abstract: We introduce a new method for ``twisting'' relative equivalences of derived categories of sheaves on two spaces over the same base. The first aspect of this is that the derived categories of sheaves on the spaces are twisted. They become derived categories of sheaves on gerbes living over spaces that are locally (on the base) isomorphic to the original spaces. Secondly, this is done in a compatible way so that the equivalence is maintained. We apply this method by proving the conjectures of Donagi and Pantev on dualities between gerbes on genus-one fibrations and comment on other applications to families of higher genus curves. We also include a related conjecture in Mirror Symmetry.


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Additional Information

Oren Ben-Bassat
Affiliation: Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Email: oren.benbassat@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04832-6
PII: S 0002-9947(09)04832-6
Received by editor(s): December 14, 2007
Published electronically: April 21, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.