Appears in collections : Research School, Méthodes géométriques et analytiques pour les points rationnels / Geometric and Analytic Methods for Rational Points

Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these cohomological tools.