Stabilization of the Witt group

In this Note, using an idea due to Thomason, we define a “homology theory” on the category of rings which satisfies excision, exactness, homotopy (in the algebraic sense) and periodicity of order 4. For regular noetherian rings, we find Balmer's higher Witt groups. For more general rings, this homology is isomorphic to the KT-theory of Hornbostel, inspired by the work of Williams. For real or complex $C^1$-algebras, we recover – up to 2 torsion – topological K-theory. To cite this article: M. Karoubi, C. R. Acad. Sci. Paris, Ser. I 342 (2006).