Unramified cohomology and Witt groups of anisotropic Pfister quadrics

Abstract

The unramified Witt group of an anisotropic conic over a field k, with char k ≠ 2, defined by the form <1,-a,-b> is known to be a quotient of the Witt group W(k) of k and isomorphic to W(k)/<1,-a,-b, ab> W(k). We compute the unramified cohomology group H k(C), where C is the three dimensional anisotropic quadric defined by the quadratic form (1,-a,-b, ab,-c) over k. We use these computations to study the unramified Witt group of C.