Emiliano Ambrosi (Ecole Polytechnique)
Specialization of representations of the étale fundamental group and applications.
Let X → S be a family of smooth projective varieties over a finitely generated field k.
For every closed point s of S we have an l-adic representation of the absolute Galois group of k on the l-adic étale cohomology of the fiber of the morphism in s. We will discuss how the image of these representations vary when s is varying in S(k). Finally we will show how these results can be used to study the specialization of Néron severi group.