2016/01/22 by Lekili, Yanki, Polishchuk, Alexander · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.1601.06141
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.