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Universal Chow group of 0-cycles and stable rationality

By Claire Voisin

Also appears in collection : Algèbre, Géométrie et Physique : une conférence en l'honneur

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.

Information about the video

  • Date of recording 25/06/2014
  • Date of publication 01/07/2014
  • Institution IHES
  • Format MP4

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