On the Witt ring of a relative projective line, by Marek Szyjewski

A ring homomorphism e^0 : W(X) --> E^+(X) from the Witt ring of a scheme X into suitable subfactor of K_0(X) and E^+(X) itself are studied for general projective bundle and split affine quadric. As an application non-extended Witt class on a projective line over a coordinate ring of affine quadric of dimension congruent to 6 mod 8 is constructed. This shows that Arason theorem that Witt ring af a projective space over a field equals to Witt ring of this field can not be generalized to projective spaces over regular rings.

Marek Szyjewski <szyjewski@gate.math.us.edu.pl>