From algebraic K-theory to hermitian K-theory

Abstract

We introduce a new morphism between algebraic and hermitian K-theory. The topological analog is the Adams operation in real K-theory. From this morphism, we deduce a lower bound for the higher algebraic K-theory of a ring A in terms of the classical Witt group of the ring A tensored by its opposite ring.

6 pages, to be published in Comptes Rendus Acad. Sci. Paris, see also http://www.math.jussieu.fr/~karoubi/