Arithmetic mirror symmetry for genus 1 curves with n marked points
| Autor: | Yanki Lekili, Alexander Polishchuk |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
General Mathematics
General Physics and Astronomy 01 natural sciences Coherent sheaf Mathematics - Algebraic Geometry Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Number Theory (math.NT) 0101 mathematics Equivalence (formal languages) Arithmetic Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics Derived category Mathematics - Number Theory 010308 nuclear & particles physics 010102 general mathematics Torus 16. Peace & justice Mathematics::Geometric Topology Mathematics - Symplectic Geometry Symplectic Geometry (math.SG) Mirror symmetry Fukaya category |
| Zdroj: | Lekili, Y & Polishchuk, A 2017, ' Arithmetic mirror symmetry for genus 1 curves with n marked points ', Selecta Mathematica, vol. 23, no. 3 . https://doi.org/10.1007/s00029-016-0286-2 |
| DOI: | 10.1007/s00029-016-0286-2 |
| Popis: | We establish a $\mathbb{Z}[[t_1,\ldots, t_n]]$-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 $t_1= \ldots =t_n=0$ gives a $\mathbb{Z}$-linear derived equivalence between the Fukaya category of the $n$-punctured torus and the derived category of perfect complexes on the standard (N\'eron) $n$-gon. We prove that this equivalence extends to a $\mathbb{Z}$-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. Comment: 53 pages, 9 figures. Minor revision. To appear in Selecta Mathematica |
| Databáze: | OpenAIRE |
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