Motivic equivalence of quadratic forms. II |
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Authors: | Oleg T Izhboldin |
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Institution: | Universit?t Bielefeld, Fakult?t für Mathematik, Postfach 100131, 33501 Bielefeld, Germany?e-mail: oleg@mathematik.uni-bielefeld.de, DE
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Abstract: | Let F be a field of characteristic ≠2 and φ be a quadratic form over F. By X
φ we denote the projective variety given by the equation φ=0. For each positive even integer d≥8 (except for d=12) we construct a field F and a pair φ, ψ of anisotropic d-dimensional forms over F such that the Chow motives of X
φ and X
ψ coincide but . For a pair of anisotropic (2
n
-1)-dimensional quadrics X and Y, we prove that existence of a rational morphism Y→X is equivalent to existence of a rational morphism Y→X.
Received: 27 September 1999 / Revised version: 27 December 1999 |
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Keywords: | Mathematics Subject Classification (1991):Primary 11E81 11E04 Secondary 19E15 |
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