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Comptes Rendus Mathématique
Volume 341, n° 6
pages 339-342 (septembre 2005)
Doi : 10.1016/j.crma.2005.07.020
Received : 24 May 2005 ;  accepted : 7 June 2005
De la K -théorie algébrique vers la K -théorie hermitienne
From algebraic K -theory to Hermitian K -theory
 

Max Karoubi
Département de mathématiques, UMR 7586 du CNRS, case 7012, université Paris 7, 2, place Jussieu, 75251 Paris cedex 05, France 

Résumé

Dans cette Note, nous introduisons un morphisme nouveau entre la K -théorie algébrique et la K -théorie hermitienne. Lʼanalogue topologique en est lʼopération dʼAdams   en K -théorie réelle. Nous en déduisons une minoration de la K -théorie algébrique supérieure dʼun anneau A en termes du groupe de Witt classique de lʼanneau  . Pour citer cet article : M. Karoubi, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Abstract

In this Note, 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  . To cite this article: M. Karoubi, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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