Poincaré institute

Reinventing rational points

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A quantitative version of the fibration method

Daniel Loughran

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.