An arithmetic refinement of homological mirror symmetry for the 2torus
An arithmetic refinement of homological mirror symmetry for the 2torus

Yanki Lekili, University of Cambridge
IAS  Simonyi Hall Seminar Room SH101
We establish a derived equivalence of the Fukaya category of the 2 torus, relative to a basepoint, with the category of perfect complexes on the Tate curve over Z. It specializes to an equivalence, over Z, of the Fukaya category of the punctured torus with perfect complexes on the nodal Weierstrass curve y^2+xy=x^3, and, over the punctured disc Z((q)), to an integral refinement of the known statement of homological mirror symmetry for the 2 torus. This is joint work with Tim Perutz.