Intégration sur les variétés -adiques
Intersection de courbes et de sous-groupes et problèmes de minoration de hauteur dans les variétés abéliennes C.M.
Nous prouvons un cas particulier de la conjecture suivante e Zilber-Pink, conjecture généralisant celle de Manin-Mumford : soit une courbe incluse dans une variété abélienne sur , qui n’est pas incluse dans une sous-variété de torsion ; l’intersection de avec la réunion de tous les sous-groupes de codimension au moins 2 est finie. Nous démontrons ici le cas où est une puissance d’une variété abélienne C.M. simple. La preuve reprend la stratégie de Rémond (suivant Bombieri-Masser-Zannier)...
Iwasawa-theory of abelian varieties at primes of non-ordinary reduction.
Kummer theory of abelian varieties and reductions of Mordell-Weil groups
Lemmes de mulitiplicités et intersections.
Lifting Galois representations and a conjecture of Fontaine and Mazur.
Local heights on Abelian varieties and rigid analytic uniformization.
Minorations de hauteurs sur les variétés abéliennes
Modularity of fibres in rigid local systems.
Non-existence of points rational over number fields on Shimura curves
Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
Non-trivial in the Jacobian of an infinite family of curves of genus 2
We give an infinite family of curves of genus 2 whose Jacobians have non-trivial members of the Tate-Shafarevich group for descent via Richelot isogeny. We prove this by performing a descent via Richelot isogeny and a complete 2-descent on the isogenous Jacobian. We also give an explicit model of an associated family of surfaces which violate the Hasse principle.
On abelian varieties associated with elliptic curves with complex multiplication
On arithmetic in Mordell-Weil groups
On cohomological systems of Galois representations
The paper contains an expanded version of the talk delivered by the first author during the conference ALANT3 in Będlewo in June 2014. We survey recent results on independence of systems of Galois representations attached to ℓ-adic cohomology of schemes. Some other topics ranging from the Mumford-Tate conjecture and the Geyer-Jarden conjecture to applications of geometric class field theory are also considered. In addition, we have highlighted a variety of open questions which can lead to interesting...
On component groups of Jacobians of Drinfeld modular curves
Let be the Jacobian variety of the Drinfeld modular curve over , where is an ideal in . Let be an exact sequence of abelian varieties. Assume , as a subvariety of , is stable under the action of the Hecke algebra End . We give a criterion which is sufficient for the exactness of the induced sequence of component groups of the Néron models of these abelian varieties over . This criterion is always satisfied when either or is one-dimensional. Moreover, we prove that the sequence...
On the arithmetic of twists of superelliptic curves
On the critical values of Hecke L-series
On the existence of dimension zero divisors in algebraic function fields defined over
On the height constant for curves of genus two
On the height constant for curves of genus two, II