Remark on the rank of elliptic curves
Igor Nikolaev
TL;DR
This paper introduces a covariant functor linking elliptic curves with complex multiplication to noncommutative tori with real multiplication and proposes a conjecture regarding the rank of elliptic curves.
Contribution
It constructs a novel functor between elliptic curves with complex multiplication and noncommutative tori with real multiplication, and formulates a new conjecture on elliptic curve ranks.
Findings
Proposes a new functor connecting elliptic curves and noncommutative tori.
Formulates a conjecture on the rank of elliptic curves.
Provides theoretical insights into the structure of elliptic curves with complex multiplication.
Abstract
A covariant functor on the elliptic curves with complex multiplication is constructed. The functor takes values in the noncommutative tori with real multiplication. A conjecture on the rank of an elliptic curve is formulated.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models