2005/09/07 by Oren Ben-Bassat, Jonathan Block, Tony Pantev · 41 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic structures and combinatorial models #Commutative property #Duality (order theory) #Equivalence (formal languages) #Fourier transform #Geometry #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Pure mathematics #Torus #hep-th #math.AG #math.QA #msc:14A20 #msc:14A22 #msc:53D55 #msc:58B34
paper · pdf · doi:10.1112/s0010437x06002636
published in Compositio Mathematica 143(02), 423-475 (Cambridge University Press) · 80 pages, LaTeX2e
arxiv created 2005/09/07 · openalex publication_date 2007/03/01 · arxiv updated 2019/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 -field direction to a formal gerbe. We show that these two deformations are Fourier–Mukai equivalent.