Non-commutative tori and Fourier-Mukai duality
Algebraic Geometry
2019-03-18 v1 High Energy Physics - Theory
Quantum Algebra
Abstract
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 these two deformations are Fourier-Mukai equivalent.
Keywords
Cite
@article{arxiv.math/0509161,
title = {Non-commutative tori and Fourier-Mukai duality},
author = {Oren Ben-Bassat and Jonathan Block and Tony Pantev},
journal= {arXiv preprint arXiv:math/0509161},
year = {2019}
}
Comments
80 pages, LaTeX2e