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

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

2008-11-14

arxiv.org/abs/0811.2260v2

Mathematics

Number Theory

short version to appear in Compositio

Scientific paper

Soit $E/\BmQ$ une courbe elliptique. Soit $D<0$ un discriminant fondamental suffisamment grand. Si $E(\bar{\BmQ})$ contient des points de Heegner de discriminant $D$, ces points engendrent un sous-groupe dont le rang est sup\'erieur \`a $\pabs{D}^{0.0009}$. Ce r\'esultat 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 $E(\bar{\BmQ})$ contains Heegner points of discriminant $D$, these points generate a subgroup of rank greater than $\pabs{D}^{0.0009}$. This result is in agreement with the conjecture of Birch and Swinnerton-Dyer.

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