Preschool
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Cyril
Demarche
:
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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.
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David
Harari
:
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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.
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Emmanuel
Peyre
:
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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.
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Damaris
Schindler
:
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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.
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