Néron models and tame ramification
Néron models from the rigid analytic viewpoint.
Néron models from the rigid analytic viewpoint
Nonabelian Hodge theory in characteristic
Given a scheme in characteristic p together with a lifting modulo p2, we construct a functor from a category of suitably nilpotent modules with connection to the category of Higgs modules. We use this functor to generalize the decomposition theorem of Deligne-Illusie to the case of de Rham cohomology with coefficients.
Non-Archimedean analytic curves in Abelian varieties.
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.
Numerical equivalence and cohomological equivalence for abelian varieties over finite fields. (Equivalence numérique et équivalence cohomologique pour les variétés abéliennes sur les corps finis.)