Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T10:53:20.392Z Has data issue: false hasContentIssue false
  • English
  • Français

AN ANALOGUE OF CIRCULAR UNITS FOR PRODUCTS OF ELLIPTIC CURVES

Published online by Cambridge University Press:  27 May 2004

Srinath Baba  and
Ramesh Sreekantan
Srinath Baba
Affiliation:
Department of Mathematics, McGill University, Montreal, Quebec H3A 2K6, Canada ([email protected])
Ramesh Sreekantan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Colaba, Mumbai 400 005, India ([email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We construct certain elements in the motivic cohomology group $H^3_{\mathcal{M}}(E\times E',\mathbb{Q}(2))$, where $E$ and $E'$ are elliptic curves over $\mathbb{Q}$. When $E$ is not isogenous to $E'$ these elements are analogous to circular units in real quadratic fields, as they come from modular parametrizations of the elliptic curves. We then find an analogue of the class-number formula for real quadratic fields, which specializes to the usual quadratic class-number formula when $E$ and $E'$ are quadratic twists.

AMS 2000 Mathematics subject classification: Primary 11F67; 14G35. Secondary 11F11; 11E45; 14G10

Keywords

motivic cohomologyclass numberBeilinson conjectures
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 1 , February 2004 , pp. 35 - 51
Copyright
Copyright © Edinburgh Mathematical Society 2004