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1 results

  • Non-commutative tori and Fourier–Mukai duality

  • O. Ben-Bassat, J. Block, T. Pantev
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 2 / March 2007
    Published online by Cambridge University Press:
    26 March 2007, pp. 423-475
    Print publication:
    March 2007
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  • The classical Fourier–Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to an equivalence between two dual objects. Both of these are generalized deformations of the complex tori. In one case, a complex torus is deformed formally in a non-commutative direction specified by a holomorphic Poisson structure. In the other, the dual complex torus is deformed in a $B$-field direction to a formal gerbe. We show that these two deformations are Fourier–Mukai equivalent.