CM elliptic curves and the Coates{Wiles Theorem

Authors

  • Martí Roset Julià McGill University

Keywords:

BSD Conjecture, Coates Wiles Theorem, L-series, elliptic curves with CM, Euler systems, ellip-tic units.

Abstract

We describe one of the few cases of the Birch and Swinnerton-Dyer Conjecture
that has been already proved, the so called Coates{Wiles Theorem. Let K be an
imaginary quadratic eld with ring of integers O and class number 1 and let E be an
elliptic curve dened over K with complex multiplication by O. The Coates{Wiles
Theorem states that if the L-series attached to E=K does not vanish at 1, then
the set of K-rational points of E is nite. We explain a proof given by Karl Rubin,
which uses the theory of Euler systems.

Keywords: BSD Conjecture, Coates Wiles Theorem, L-series, elliptic curves with CM, Euler systems, ellip-tic units.

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How to Cite

Roset Julià, M. (2020). CM elliptic curves and the Coates{Wiles Theorem. Reports@SCM, 5(1), 45–56. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/140661

Issue

Vol. 5 No. 1 (2020)

Section

Articles

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