Homotopy invariance of coherent Witt groups

 We prove the following general homotopy invariance theorem for coherent Witt groups: Let be a flat morphism of separated Gorenstein schemes of finite Krull dimension with affine fibers,i.e. π⁻¹(y) is an affine space over the residue field k(y) for all yY, then the induced homomorphism of coherent Witt groups is an isomorphism. As an application we calculate the (classical) Witt group of the affine hyperbolic sphere over a regular local ring. Received: 22 August 2001; in final form: 22 June 2002 / Published online: 1 April 2003