### Le théorème de périodicité en K-théorie hermitienne, by Max Karoubi (Paris University)

Bott periodicity plays an important role in topological K-theory. The purpose
of this paper is to extend the periodicity theorem in a discrete context, where
all classical groups are involved and not just the general linear group. The
present paper generalizes previous results of the author [K1] and [K2], where 2
was assumed to be invertible in the ring.
For the proof, two important ideas have to be mentioned. The first one is due
to Ranicki [R] who introduced a kind of "enlarged" orthogonal group. The second
one is a genuine cup-product between quadratic forms due to Clauwens [C]. As an
example of results obtained, we prove that the higher Witt groups of a finite
field of characteristic 2 are all isomorphic to Z/2. They generalize in some
sense the Dickson and Arf invariants.

Max Karoubi (Paris University) <max.karoubi@gmail.com>