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Cycles of codimension 3 on a projective quadric

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Abstract

Let X be a nonsingular quadratic hypersurface in a projective space over an arbitrary field (of characteristic not two) and let CHpX be a Chow group of codimension p, that is, a group of classes of codimension p cycles on X with respect to rational equivalency. It is proved that torsion in CH3X is either trivial or is a second order group. Torsion in CHpX, when p≠ 3, was studied earlier in RZhMat 1990, 9 A334 and 10 A389.

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Authors
  1. N. A. Karpenko
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 114–123, 1991.

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Karpenko, N.A. Cycles of codimension 3 on a projective quadric. J Math Sci 63, 678–682 (1993). https://doi.org/10.1007/BF01097981

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