|Joint IAS-PU Symplectic Geometry Seminar|
|Topic:||An Arithmetic Refinement of Homological Mirror Symmetry for the 2-Torus|
|Affiliation:||University of Cambridge|
|Date:||Friday, November 9|
|Time/Room:||4:30pm - 5:30pm/S-101|
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.