Let and be projective quadrics corresponding to quadratic forms and over a field . If is isomorphic to in the category of Chow motives, we say that and are motivic isomorphic and write . We show that in the case of odd-dimensional forms the condition is equivalent to the similarity of and . After this, we discuss the case of even-dimensional forms. In particular, we construct examples of generalized Albert forms and such that and .
Cite this article
Oleg T. Izhboldin, Motivic equivalence of quadratic forms. Doc. Math. 3 (1998), pp. 341–351DOI 10.4171/DM/50