Non-commutative tori and Fourier-Mukai duality

O. Ben-Bassat, J. Block, T. Pantev

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)423-475
Number of pages53
JournalCompositio Mathematica
Issue number2
StatePublished - Mar 2007
Externally publishedYes


  • Analytic sheaves
  • Deformation quantization
  • Fourier-Mukai transform
  • Gerbe

ASJC Scopus subject areas

  • Algebra and Number Theory


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