Resumen de Arithmetic mirror symmetry for genus 1 curves with n marked points

Yanki Lekili, Alexander Polishchuk

• We establish a Z[[t1,..., tn]]-linear derived equivalence between the relative Fukaya category of the 2-torus with n distinct marked points and the derived category of perfect complexes on the n-Tate curve. Specialising to t1 =···= tn = 0 gives a Z-linear derived equivalence between the Fukaya category of the n-punctured torus and the derived category of perfect complexes on the standard (Néron) n-gon. We prove that this equivalence extends to a Z-linear derived equivalence between the wrapped Fukaya category of the n-punctured torus and the derived category of coherent sheaves on the standard n-gon. The corresponding results for n = 1 were established in Lekili and Perutz (Arithmetic mirror symmetry for the 2-torus (preprint) arXiv:1211.4632, 2012).