Texas A&M University, Department of
Mathematics, 216 Milner Hall, 20th of October 2004, 3:00-3:50
Groups and Dynamics Seminar
Some conjectures on
quadratic forms proved by Steenrod operations
Nikita Karpenko of Université
d'Artois, Lens, France, and Institute for Advanced Study at Princeton
The (modulo 2) Steenrod operations, well known for a long time in
topology, were recently constructed in an algebro-geometric context by
Voevodsky. They provided the main ingredient of his proof of the Milnor
conjecture. We use the Steenrod operations on Chow groups to prove some
other conjectures on quadratic forms: the Hoffmann conjecture on values
of the higher Witt indices, the Rehmann conjecture on minimality of the
excellent height, and the Vishik conjecture on dimensions of quadratic
forms with trivial cohomological invariants.