Abstract : We show that over any uncountable field of characteristic different from two, a very general hypersurface of dimension n [is greater than 2] and degree at least log2(n)+2 is not stably rational. This significantly improves earlier results of Kollár and Totaro. As a byproduct of our proof, we obtain new counterexamples to the integral Hodge conjecture, answering a question of Voisin and Colliot-Thélène - Voisin.
Recording during the meeting "Birational Geometry and Hodge Theory" the February 14, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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