Variation of periods modulo in arithmetic dynamics.
Variation of the canonical height on elliptic surfaces I: Three examples.
Variation of the reduction type of elliptic curves under small base change with wild ramification
We study the variation of the reduction type of elliptic curves under base change. A complete description of the variation is given when the base field is the p-adic field and the base change is of small degree.
Variation of the root number in families of elliptic curves
Variations on a theme of Runge: effective determination of integral points on certain varieties
We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge’s theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge’s theorem due to Bombieri. We then take up the study of how Runge’s method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application of our...
Variétés abéliennes et invariants arithmétiques
Dans la continuité de nos travaux précédents, nous étudions un analogue, pour le modèle de Néron d’une variété abélienne semi-stable sur un corps de nombres, du class-invariant homomorphism introduit par M. J. Taylor, qui nous permet de mesurer la structure galoisienne de certains torseurs.
Variétés de Drinfeld compactes
Variétés stablement rationnelles non rationnelles
Variétés unirationnelles non rationnelles
Variétés unirationnelles non rationnelles: au-delà de l'example d'Artin et Mumford.
Varieties in positive characteristic with trivial tangent bundle
Varieties of small degree over finite fields.
Visualizing elements in the Shafarevich-Tate group.
Volcanoes of l-isogenies of elliptic curves over finite fields: The case l=3.
This paper is devoted to the study of the volcanoes of ℓ-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper lies on the relationship between the ℓ-Sylow subgroup of an elliptic curve and the level of the volcano where it is placed. The particular case ℓ = 3 is studied in detail, giving an algorithm to determine the volcano of 3-isogenies of a given elliptic curve. Experimental results...
Weak approximation and non-abellian fundamental groups
Weak Néron models for cubic polynomial maps over a non-Archimedean field
Weakly quasihomogeneous hypersurface singularities in positive characteristic.
Weierstrass points in characteristic p.
Weierstrass points on arithmetic surfaces.
Weights in rigid cohomology applications to unipotent -isocrystals