Arithmetic mirror symmetry for genus 1 curves with n marked points

• Yankı Lekili ^[1] ; Alexander Polishchuk ^[2]
  1. [1] King's College London

     King's College London

     Reino Unido

     
  2. [2] University of Oregon
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 1851-1907
• Idioma: inglés
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• Resumen

  • 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).