Dima Arikin

Quantizations of dual abelian varieties

Let A and A' be dual abelian varieties, so that A' is the space of topologically trivial line bundles on A. In general, A and A' are not isomorphic, but they are always related by the Fourier-Mukai transform, which is an equivalence between the derived categories of A and A'. We will explain another relation between dual abelian varieties: to a deformation quantization of A, there corresponds a dual (in some sense) deformation quantization of A'.