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Proceedings of the American Mathematical Society

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Zero cycles on quadric hypersurfaces


Author: Richard G. Swan
Journal: Proc. Amer. Math. Soc. 107 (1989), 43-46
MSC: Primary 14C25; Secondary 11E04
MathSciNet review: 979219
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Abstract: Let $ X$ be a projective quadric hypersurface over a field of characteristic not 2. It is shown that the Chow group $ {A_0}(X)$ of 0-cycles modulo rational equivalence is infinite cyclic, generated by any point of minimal degree.


References [Enhancements On Off] (What's this?)

  • [1] William Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984. MR 732620
  • [2] T. Y. Lam, The algebraic theory of quadratic forms, W. A. Benjamin, Inc., Reading, Mass., 1973. Mathematics Lecture Note Series. MR 0396410
  • [3] Richard G. Swan, Vector bundles, projective modules and the 𝐾-theory of spheres, Algebraic topology and algebraic 𝐾-theory (Princeton, N.J., 1983), Ann. of Math. Stud., vol. 113, Princeton Univ. Press, Princeton, NJ, 1987, pp. 432–522. MR 921488
  • [4] Richard G. Swan, 𝐾-theory of quadric hypersurfaces, Ann. of Math. (2) 122 (1985), no. 1, 113–153. MR 799254, 10.2307/1971371

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DOI: https://doi.org/10.1090/S0002-9939-1989-0979219-2
Article copyright: © Copyright 1989 American Mathematical Society