Variations on a Theme of Rationality of Cycles

  title={Variations on a Theme of Rationality of Cycles},
  author={Nikita A. Karpenko},
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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