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

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

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Yanki Lekili, University of Cambridge
IAS - Simonyi Hall Seminar Room SH-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. 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.