Équivalences rationnelle et numérique sur certaines variétés de type abélien sur un corps fini
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.
This is a brief exposition on the uses of non-commutative fundamental groups in the study of Diophantine problems.