Institut de Mathématiques de Jussieu
PARIS, 9  17 juin 2011
Organisateurs / Organizers
F. DÉGLISE (CNRS  Paris 13), V. MAILLOT (CNRS  IMJ),
J. WILDESHAUS (Paris 13)
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 Ktheories of algebraic
topology.
The second one appeared about one year later (December 1996).
The use of Morava Ktheories 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).

