An analogue of cyclotomic units for products of elliptic curves

2001/10/17 by Srinath Baba, Baba, Srinath, Ramesh Sreekantan +1
Mathematics · #11G16 #11G18 #14C25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.NT #msc:11G16 #msc:11G18 #msc:14C25

paper · pdf · doi:10.48550/arxiv.math/0110180

25 pages. Typos and a statement of a theorem of Scholl and Harris corrected

openalex publication_date 2001/10/17 · arxiv created 2001/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct certain elements in the integral motivic cohomology group H³_{\cal M}(E × E',\Q(2))_\ZZ, where E and E' are elliptic curves over \Q. When E is not isogenous to E' these elements are analogous to `cyclotomic units' in real quadratic fields as they come from modular parametrisations of the elliptic curves. We then find an analogue of the class number formula for real quadratic fields. Finally we use the Beilinson conjectures for E × E' to deduce them for products of n elliptic curves. A certain amount of this paper is expository in nature.

Related

• Modularity of elliptic curves over cyclotomic ℤ_p-extensions of real quadratic fields
• Algebraic Cycles and values of Green's functions
• Root numbers of a family of elliptic curves and two applications
• Elliptic analogue of irregular prime numbers for the pⁿ-division fields of the curves y² = x³-(s⁴+t²)x
• Elliptic curves with complex multiplication and abelian division fields