Selmer groups of Hecke characters and Chow groups of self products of CM elliptic curves

1999/01/11 by Jonathan Dee, Dee, Jonathan · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/9901155

arxiv created 1999/01/11 · openalex publication_date 1999/01/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We bound Selmer groups attached to Grossencharacters of CM elliptic curves by the appropriate L-value. Our method is to use Kato's explicit reciprocity law and the Main Conjecture as proved by Rubin. These results are then used together with work of Han and fundamental results of Nekovar to bound the torsion in the image of the p-adic cycle class map for self products of CM elliptic curves. Our results are valid for Chow groups of arbitrary codimension for almost all p.

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