Variations on a Theme of Rationality of Cycles

@inproceedings{Karpenko2011VariationsOA,
  title={Variations on a Theme of Rationality of Cycles},
  author={Nikita A. Karpenko},
  year={2011}
}
We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ̸= 2. Our weak versions are still sufficient for existing applications. In particular… CONTINUE READING

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Showing 1-10 of 11 references

Fields of u-invariant 2 + 1. In Algebra, arithmetic, and geometry: in honor of Yu. I

  • A. Vishik
  • Manin. Vol. II, vol. 270 of Progr. Math. Birkha…
  • 2009
Highly Influential
4 Excerpts

Fields of u - invariant 2 r + 1

  • A. Vishik
  • Algebra , arithmetic , and geometry : in honor of…
  • 2009

Symmetric operations in algebraic cobordism

  • A. Vishik
  • Adv. Math. 213,
  • 2007
1 Excerpt

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