An Arithmetic Refinement of Homological Mirror Symmetry for the 2-Torus

Joint IAS-PU Symplectic Geometry Seminar
Topic:An Arithmetic Refinement of Homological Mirror Symmetry for the 2-Torus
Speaker:Yanki Lekili
Affiliation:University of Cambridge
Date:Friday, November 9
Time/Room:4:30pm - 5:30pm/S-101
Video Link:https://video.ias.edu/jointiaspu/lekili

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[[q]]. 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.