Corps engendré par les points de 13-torsion des courbes elliptiques
Correspondance
Correspondances de Hecke, action de Galois et la conjecture d’André–Oort
Soient une variété de Shimura, fermée et irréductible et un ensemble Zariski dense de points spéciaux. Selon la conjecture d’André–Oort, est une sous-variété de type Hodge. Par exemple, si est un espace de modules de variétés abéliennes, est un ensemble de points correspondant à des variétés de type CM et doit paramétrer des variétés abéliennes munies de certaines classes de Hodge. En utilisant les actions de l’algèbre de Hecke et du groupe de Galois, Edixhoven et Yafaev montrent certains...
Corrigendum - Points entiers et théorèmes de Bertini arithmétiques
Corrigendum to "Distribution of the traces of Frobenius on elliptic curves over function fields" (Acta Arith. 106 (2003), 255-263)
Corrigendum to: Improved upper bounds for the number of points on curves over finite fields
Corrigendum to the paper "The number of solutions of the Mordell equation" (Acta Arith. 88 (1999), 173–179)
Counting elliptic curves of bounded Faltings height
We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².
Counting points in medium characteristic using Kedlaya's algorithm.
Counting points of fixed degree and bounded height
Counting points on elliptic curves over finite fields
We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic polynomial...
Counting rational points on a certain exponential-algebraic surface
We study the distribution of rational points on a certain exponential-algebraic surface and we prove, for this surface, a conjecture of A. J. Wilkie.
Counting rational points on cubic and quartic surfaces
Counting rational points on del Pezzo surfaces with a conic bundle structure
For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.
Counting rational points on hypersurfaces of low dimension
Courbes algébriques de genre ≥ 2 possédant de nombreux points rationnels
Courbes Elliptiques et 2 - Extensions Abeliennes
Courbes elliptiques et formes modulaires de poids 3/2
Covering collections and a challenge problem of Serre
Coverings of Singular curves over Finite Fields.