La conjecture de Mordell
La -équivalence sur les tores
La R-équivalence sur les groupes algébriques réductifs définis sur un corps global
Lagrangian 4-planes in holomorphic symplectic varieties of K3[4]-type
We classify the cohomology classes of Lagrangian 4-planes ℙ4 in a smooth manifold X deformation equivalent to a Hilbert scheme of four points on a K3 surface, up to the monodromy action. Classically, the Mori cone of effective curves on a K3 surface S is generated by nonnegative classes C, for which (C, C) ≥ 0, and nodal classes C, for which (C, C) = −2; Hassett and Tschinkel conjecture that the Mori cone of a holomorphic symplectic variety X is similarly controlled by “nodal” classes C such that...
Lang’s conjecture in characteristic : an explicit bound
Lang's Conjectures, Fibered Powers, and Uniformity.
Le spectre réel et la topologie des variétés algébriques sur un corps réel clos
L'équivalence rationnelle sur les points fermés des surfaces rationnelles fibrées en coniques
L'équivalence rationnelle sur les tores.
Les points exceptionnels rationnels sur certaine cubique du premier genre
Les points rationnels de
Linear forms on abelian varieties over local fields
Linking the conjectures of Artin-Tate and Birch-Swinnerton-Dyer
Local Diophantine Properties of Shimura Curves.
Local-global divisibility of rational points in some commutative algebraic groups
Let be a commutative algebraic group defined over a number field . We consider the following question:Let be a positive integer and let . Suppose that for all but a finite number of primes of , we have for some . Can one conclude that there exists such that ?A complete answer for the case of the multiplicative group is classical. We study other instances and in particular obtain an affirmative answer when is a prime and is either an elliptic curve or a torus of small dimension...
Local-global principle for certain biquadratic normic bundles
Let X be a proper smooth variety having an affine open subset defined by the normic equation over a number field k. We prove that: (1) the failure of the local-global principle for zero-cycles is controlled by the Brauer group of X; (2) the analogue for rational points is also valid assuming Schinzel’s hypothesis.