Dualization in algebraic K-theory and invariant e^1 of quadratic forms over schemes, by Marek Szyjewski

This is a report on the joint work with S. Nenashev. For any exact category M with duality D there is a subgroup I(M,D) of Witt group W(M,D) (kernel of e0 : W(M,D) ----> E0(M,D) defined in earlier papers).

A homomorphism e1 : I(M,D) ----> k1(M,D) is defined, where k1(M,D) is appropriate subfactor of K1(M). In the classical case of Witt ring of a field it is discriminant.

The construction yields that explixcit computations, e.g. discriminants of symmetric bilinear forms with values in OX(-1) on a conic are computed.

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