A purity theorem for the Witt group

Let A be a regular local ring and K its field of tractions. We denote by W the Witt group functor that classifies quadratic spaces. We say that purity holds for A if W(A) is the intersection of all W(A(p)) subset of W(K), as p runs over the height-one prime ideals of A. We prove purity For every reg ular local ring containing a field of characteristic not equal 2. The quest ion of purity and of the injectivity of W(A) into W(K) for arbitrary regula r local rings is still open. (C) Elsevier, Paris.