Appears in collection : 2019 - T2 - WS1 - Rational Points on Fano and Similar Varieties

Harpaz and Wittenberg have made spectacular progress on the fibration method, with regards to the study of the Brauer-Manin obstruction to the Hasse principle on rationally connected varieties. In this talk I present a quantitative version of their method, which allows one to count the number of rationally connected varieties in certain families with a rational point, even if the Brauer group is non-constant. This is joint work with Lilian Matthiesen.