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Title:
An Arithmetic Refinement of Homological Mirror Symmetry for the 2-Torus
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Abstract:
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.
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