Non-commutative compactifications and elliptic curves

Abstract

We study non-commutative degenerations of elliptic curves over local fields. The corresponding objects are close relatives of non-commutative tori of Connes and Rieffel.

Few corrections added

References in corpus (5)

• Morita equivalence and duality
• Finite in All Directions
• Mirror symmetry for abelian varieties
• Number theory and dynamical systems on foliated spaces
• Theta-functions on noncommutative tori

Cited by in corpus (7)

• Categories of holomorphic vector bundles on noncommutative two-tori
• Noncommutative tori and the Riemann-Hilbert correspondence
• Noncommutative geometry of algebraic curves
• On complex and noncommutative tori
• Riemann surfaces and AF-algebras
• On a Teichmueller functor between the categories of complex tori and the Effros-Shen algebras
• Remark on the rank of elliptic curves