Appears in collections : Algèbre, Géométrie et Physique : une conférence en l'honneur, Distinguished women in mathematics

Much work has been done in the 70's to solve the Lüroth problem of distinguishing unirational from rational (or stably rational) varieties. For 3-dimensional unirational varieties, the only stable birational invariant used up to now has been the Artin-Mumford invariant.We showusing the universal Chow group of zero-cycles that some unirational threefolds with trivial Artin-Mumford invariant are not stably rational.Some of these examples have the following property: they do not admit a universal codimension 2 cycle,which prevents their stable rationality and exhibits a new phenomenon in the theory of algebraic cycles.