Motivic equivalence of quadratic forms

  • Oleg T. Izhboldin

    98904 Russia
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Let XϕX_\phi and XψX_\psi be projective quadrics corresponding to quadratic forms ϕ\phi and ψ\psi over a field FF. If XϕX_\phi is isomorphic to XψX_\psi in the category of Chow motives, we say that ϕ\phi and ψ\psi are motivic isomorphic and write ϕ\msimψ\phi\msim\psi. We show that in the case of odd-dimensional forms the condition ϕ\msimψ\phi\msim\psi is equivalent to the similarity of ϕ\phi and ψ\psi. After this, we discuss the case of even-dimensional forms. In particular, we construct examples of generalized Albert forms q1q_1 and q2q_2 such that q1\msimq2q_1\msim q_2 and q1≁q2q_1\not\sim q_2.

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Oleg T. Izhboldin, Motivic equivalence of quadratic forms. Doc. Math. 3 (1998), pp. 341–351

DOI 10.4171/DM/50