Équations différentielles -adiques et dégénérescence de groupes de Hodge
Equations for Endomorphisms of Abelian Varieties.
Équidistribution des sous-variétés de petite hauteur
On montre dans cet article que le théorème d’équidistribution de Szpiro-Ullmo-Zhang concernant les suites de petits points sur les variétés abéliennes s’étend au cas des suites de sous-variétés. On donne également une version quantitative de ce résultat.
Equidistribution of small subvarieties of an Abelian variety.
Erratum à «Sur une conjecture de Kottwitz au bord»
Essential dimension of moduli of curves and other algebraic stacks
In this paper we consider questions of the following type. Let be a base field and be a field extension. Given a geometric object over a field (e.g. a smooth curve of genus ), what is the least transcendence degree of a field of definition of over the base field ? In other words, how many independent parameters are needed to define ? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete answer to...
Estimating isogenies on elliptic curves.
Étale cohomology and reduction of abelian varieties
In this paper we study the étale cohomology groups associated to abelian varieties. We obtain necessary and sufficient conditions for an abelian variety to have semistable reduction (or purely additive reduction which becomes semistable over a quadratic extension) in terms of the action of the absolute inertia group on the étale cohomology groups with finite coefficients.
Etale coverings of a Mumford curve
Let the field be complete w.r.t. a non-archimedean valuation. Let be a Mumford curve, i.e. the irreducible components of the stable reduction of have genus 0. The abelian etale coverings of are constructed using the analytic uniformization and the theta-functions on . For a local field one rediscovers . Frey’s description of the maximal abelian unramified extension of the field of rational functions of .
Étude sur les relations algébriques entre les fonctions hyperelliptiques de genre 3
Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli.
Examples of abelian surfaces in P4.
Exceptional Hodge Classes on Certain Abelian Varieties.
Explicit bounds for split reductions of simple abelian varieties
Let be an absolutely simple abelian variety over a number field; we study whether the reductions tend to be simple, too. We show that if is a definite quaternion algebra, then the reduction is geometrically isogenous to the self-product of an absolutely simple abelian variety for in a set of positive density, while if is of Mumford type, then is simple for almost all . For a large class of abelian varieties with commutative absolute endomorphism ring, we give an explicit upper bound...
Explicit p-adic theta function.
Extension universelle d'une variété abélienne et hauteurs des points de torsion
Extensions of Abelian Varieties Defined Over a Finite Field.