Triviality of $X_{\mathrm{split}} (N) (Q )$ for certain congruence classes of the level
Language
en
Article de revue
This item was published in
Comptes rendus de l'Académie des sciences. Série I, Mathématique. 2003, vol. 5, n° 336, p. 377-380
Elsevier
English Abstract
We give a criterion to check if, given a prime number N, the only rational points of the modular curve $X_{\mathrm{split}} (N)$ are trivial ({\it i.e.} cusps or points furnished by complex multiplication). We then prove ...Read more >
We give a criterion to check if, given a prime number N, the only rational points of the modular curve $X_{\mathrm{split}} (N)$ are trivial ({\it i.e.} cusps or points furnished by complex multiplication). We then prove that this criterion is verified for N large enough and satisfying explicit congruences.Read less <
Keywords
points de Gross-Heegner
Courbes elliptiques
courbes modulaires
points rationnels
représentations galoisiennes
points de Gross-Heegner.
Origin
Hal imported