Poincaré institute

Reinventing rational points

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in Luminy

Cyril Demarche  :
Cohomological obstructions to local-global 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 local-to-global principles for rational points

A general survey about Galois and étale cohomology, arithmetic duality theorems, and Poitou-Tate exact sequences, with an emphasis on applications to local-to-global 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.