Minoration du rang des courbes elliptiques sur les corps de classes de Hilbert

2008/11/14 by Nicolas Templier, Templier, Nicolas · 1 citation
Mathematics · #11G15 #11G40 #11G50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT #msc:11G15 #msc:11G40 #msc:11G50

paper · pdf · doi:10.48550/arxiv.0811.2260

short version to appear in Compositio

openalex publication_date 2008/11/14 · arxiv created 2010/05/15 · arxiv updated 2010/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Soit E/\BmQ une courbe elliptique. Soit D<0 un discriminant fondamental suffisamment grand. Si E(\BmQ) contient des points de Heegner de discriminant D, ces points engendrent un sous-groupe dont le rang est supérieur à \pabsD^0.0009. Ce résultat est en accord avec la conjecture de Birch et Swinnerton-Dyer. --- Let E/\BmQ be an elliptic curve. Let D<0 be a sufficiently large fundamental discriminant. If E(\BmQ) contains Heegner points of discriminant D, these points generate a subgroup of rank greater than \pabsD^0.0009. This result is in agreement with the conjecture of Birch and Swinnerton-Dyer.

Citations

• Nonvanishing theorems for L-functions of modular forms and their derivatives
• Modular Elliptic Curves and Fermat's Last Theorem

Cited by

• Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields

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