### 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
e^{0} : W(M,D) ----> E^{0}(M,D) defined in earlier
papers).

A homomorphism e^{1} : I(M,D) ----> k_{1}(M,D)
is defined, where k_{1}(M,D) is appropriate subfactor of
K_{1}(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
O_{X}(-1) on a conic are computed.

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