### Chow rings of excellent quadrics, by Nobuaki Yagita

Let k be a field of ch(k)=0. A quadratic form q over k is called excellent if
for every field extension K/k, the anisotropic part of the form q|K is defined
over k. Pfister forms, norm forms, and every forms over R are typical examples
of excellent forms. A quadric X defined by an excellent form q is called
excellent. The structure of the motive M(X) is wellknown by Rost, Hoffmann,
Karpenko, Merkurjev. So we still know the additive structure of the Chow ring
CH(X). In this paper, we determine the multiplicative structure for each
anisotropic excellent quadric, by using algebraic cobordism theory. The ring
structure depends only on dim(X).

Nobuaki Yagita <yagita@mx.ibaraki.ac.jp>