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).

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