Workshop

This workshop will explore the various ways in which cohomology gives information on the existence and density of rational points. Here are the main topics to be covered. Étale cohomology of varieties over number fields: the Brauer-Manin obstruction and beyond. Étale cohomology of varieties over finite fields: as an example, Esnault's result that smooth rationally connected varieties over a finite field have a rational point. Coherent cohomology, deformation methods: applications to varieties over function fields in one or two variables over the complex field, also to varieties over finite and local fields. Arakelov geometry, algebraic geometry over the algebraic closure of the rationals, connexions with hyperbolicity, distribution of algebraic points of small height.