Quantum Elliptic Curves I: Algebraic Case

2025/12/07 by Larsen, Michael J., Lunts, Valery
#14A22 (Primary) 16S35 #14H52 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.06936

Abstract

A complex elliptic curve E can be defined as the quotient of the analytic space ℂ^* by a discrete action of the cyclic group q^ℤ for \vert q\vert ≠ 1. We study the boundary case when \vert q\vert =1, which leads to the notion of a quantum elliptic curve and a conjectural equivalence of categories that one might call a noncommutative GAGA.

Citations

• Thick subcategories on weighted projective curves and nilpotent representations of quivers
• Thick subcategories on curves

Related

• Quantum dynamics of elliptic curves
• Conformal field theory and integrable systems associated with elliptic curves
• Commuting differential and difference operators associated to complex curves, II
• Enumerative geometry via elliptic stable envelope
• Quantum curves and topological recursion