Rational points on certain quintic hypersurfaces
Rational points on compact subgroups of algebraic groups. (Points rationnels sur les sous-groupes compacts des groupes algébriques.)
Rational points on curves
This is an extended version of an invited lecture I gave at the Journées Arithmétiques in St. Étienne in July 2009.We discuss the state of the art regarding the problem of finding the set of rational points on a (smooth projective) geometrically integral curve over . The focus is on practical aspects of this problem in the case that the genus of is at least , and therefore the set of rational points is finite.
Rational points on elliptic curves over Q in elementary abelian 2-extensions of Q.
Rational points on K3 surfaces: A new canonical height.
Rational points on K3 surfaces in ...x...x... .
Rational points on modular curves and abelian varieties.
Rational points on some elliptic surfaces
Rational points on some pencils of conics with 6 singular fibres
Rational points on the modular curves
Rational points on twists of X₀(63)
Rational points on and quadratic -curves
The rational points on in the case where is a composite number are considered. A computational study of some of the cases not covered by the results of Momose is given. Exceptional rational points are found in the cases and and the -invariants of the corresponding quadratic -curves are exhibited.
Rational points on .
Rational torsion points on elliptic curves over number fields
Rational torsion points on Jacobians of modular curves
Let p be a prime greater than 3. Consider the modular curve X₀(3p) over ℚ and its Jacobian variety J₀(3p) over ℚ. Let (3p) and (3p) be the group of rational torsion points on J₀(3p) and the cuspidal group of J₀(3p), respectively. We prove that the 3-primary subgroups of (3p) and (3p) coincide unless p ≡ 1 (mod 9) and .
Rationale Punkte auf Fermatkurven und getwisteten Modulkurven.
Rationale Punkte über eine algebraische Kurve (points rationnels sur une courbe algébrique)
Rationalité de valeurs spéciales de certaines fonctions L
Rationalité des fonctions des variétés algébriques
Rationalité et valeurs de fonctions en cohomologie cristalline
Dans l’exposé Bourbaki 409, Katz conjecture la méromorphie -adique de la fonction attachée à une variété lisse sur un corps fini () et à un -cristal sur . Si est propre et lisse sur nous prouvons que est rationnelle et fournie par l’expression habituelle utilisant l’action du Frobenius sur la cohomologie cristalline à coefficients dans ; ce résultat n’était connu, via les “conjectures de Weil”, que pour des -cristaux unités particuliers: ceux provenant d’une représentation de...