On the Witt group of the punctured spectrum of a regular semilocal ring

Abstract Let be a regular semilocal ring of dimension which contains , the number of maximal ideals of which are assumed to be all of the same height, and the punctured spectrum of , that is, without the maximal ideals. We show that the Witt ring of has non‐trivial generators as ‐algebra, which satisfy for all . If is integral, then these generators become trivial over the fraction field of . In particular, the natural morphism is not injective.