Twisting derived equivalences

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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.

Original languageEnglish
Pages (from-to)5469-5504
Number of pages36
JournalTransactions of the American Mathematical Society
Issue number10
StatePublished - Oct 2009
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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