École d'été / Summer School Motives and Milnor conjecture

Institut de Mathématiques de Jussieu

PARIS, 9 - 17 juin 2011

Organisateurs / Organizers


Comité scientifique / Scientific committee

D.-C. CISINSKI (Toulouse III), N. KARPENKO (Paris 6), M. LEVINE (Duisbourg - Essen), D. RÖSSLER (CNRS - Toulouse III)


Voevodsky has given two different proofs of the Milnor conjecture, based on the same principle but differing in the tools involved to obtain the central point (actually the final step). The first one appeared in June 1995 and was based on the conjectural existence of a geometrical analog of the Morava K-theories of algebraic topology. The second one appeared about one year later (December 1996). The use of Morava K-theories was replaced by Margolis motivic cohomology, which is defined using certain operations on motivic cohomology called Steenrod operations by analogy with the classical one acting on singular cohomology. The proof was finally published seven years later. It is based on the second approach together with some modifications.

As a first objective of the summer school, we want to provide the audience an introduction to the homotopy theory of schemes and to the theory of mixed motives. The second objective is to give a detailed overview of the proof of the Milnor conjecture, as an illustration of the theories introduced in the first part.

Conférenciers / Speakers : A. Asok (University of Southern California), J. Ayoub (CNRS - Université Paris 13, University of Zürich), S. Gille (University of München), B. Klingler (Université Paris 7), A.S. Merkurjev (University of California at Los Angeles), P.A. Ostvaer (Oslo University), A. Quéguiner (Université Paris 13, UPEC), J. Riou (Université d'Orsay), O. Röndigs (University of Osnabrück).