Non rationalité stable sur les corps quelconques

Abstract

This is a survey on (lack of) stable rationality over arbitrary fields (including algebraically closed fields). Topics addressed include: Rationality and unirationality, R-equivalence on rational points, Chow groups of zero-cycles, Galois action on the Picard group, Brauer group, higher unramified cohomology, global differentials, specialisation method (via R-equivalence), geometrically rational surfaces, cubic hypersurfaces.

Notes prepared for the Winter School "Birational geometry of hypersurfaces" held at Palazzo Feltrinelli, Gargagno del Garda, Italia, 19-23 March 2018. Language: French