Homological Mirror Symmetry in Dimension One
Bernd Kreussler
TL;DR
This paper completes the proof of a weak version of Kontsevich's homological mirror symmetry conjecture for elliptic curves by considering all morphisms, not just transversal ones, establishing the conjectured categorical equivalence.
Contribution
It extends previous work by proving the full conjectured equivalence of categories for elliptic curves, including non-transversal morphisms.
Findings
Confirmed the categorical equivalence for elliptic curves
Extended the proof to include all morphisms, not only transversal
Completed the proof of a weak version of the conjecture
Abstract
In this paper we complete the proof began by A. Polishchuk and E. Zaslow (math.AG/9801119) of a weak version of Kontsevich's homological mirror symmetry conjecture for elliptic curves. The main difference to the work of Polishchuk and Zaslow is that we consider morphisms between any pair of objects, not only in the transversal case. This enables us to show the conjectured equivalence of categories.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models