École préparatoire

Cyril
Demarche
:

Cohomological obstructions to localglobal principles
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.

David
Harari
:

Galois cohomology, arithmetic duality and obstructions to localtoglobal principles for rational points
A general survey about Galois and étale cohomology, arithmetic duality theorems, and PoitouTate exact sequences, with an emphasis on applications to localtoglobal principles.

Emmanuel
Peyre
:

Points of bounded height
These talks will start with an introduction to the notion of heights before giving a survey on the program of Manin about the asymptotic behaviour
of rational points of bounded height on varieties.

Damaris
Schindler
:

Interactions of analytic number theory and geometry
A general introduction to the state of the art in counting of rational and integral points on varieties, using various analytic methods with the Brauer–Manin obstruction.
