Twisting derived equivalences

Ben-Bassat, Oren

doi:10.1090/S0002-9947-09-04832-6

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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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