The Groups H3(F(X)/FM) and CH2(X) for Generic Splitting Varieties of Quadratic Forms |
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Authors: | Oleg T Izhboldin |
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Institution: | (1) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany |
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Abstract: | Let F be a field of characteristic different from 2 and be a quadratic form over F. Let X be an arbitrary projective homogeneous generic splitting variety of . For example, we can take X to be equal to the variety X,m of totally isotropic m-dimensional subspaces of V, where V is the quadratic space corresponding to and <
dim V. In this paper, we study the groups CH2(X) and H3(F(X)/F) = ker(H
3(F) H
3(F(X))). One of the main results of this paper claims that the group Tors CH2(X) is always zero or isomorphic to
. In many cases we prove that Tors CH2(X) = 0 and compute the group H
3(F(X)/F) completely. As an application of the main results, we give a criterion of motivic equivalence of eight-dimensional forms except for the case where the Schur indices of their Clifford algebras equal 4. |
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Keywords: | Quadratic form Galois cohomology Chow groups |
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