Variations on a theme of rationality of cycles |
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Authors: | Nikita A Karpenko |
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Institution: | 1228. Institut de Mathématiques de Jussieu, UPMC Sorbonne Universités, 4 Place Jussieu, Paris, 75020, France
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Abstract: | 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, Vishik’s construction of fields of u-invariant 2 r + 1, for r ≥ 3, is extended to arbitrary characteristic ≠ 2. |
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