Displaying similar documents to “Around rationality of cycles”

Variations on a theme of rationality of cycles

Nikita Karpenko (2013)

Open Mathematics

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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,...

Holes in I n

Nikita A. Karpenko (2004)

Annales scientifiques de l'École Normale Supérieure

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Transcendence degree of zero-cycles and the structure of Chow motives

Sergey Gorchinskiy, Vladimir Guletskiĭ (2012)

Open Mathematics

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In the paper we introduce a transcendence degree of a zero-cycle on a smooth projective variety X and relate it to the structure of the motive of X. In particular, we show that in order to prove Bloch’s conjecture for a smooth projective complex surface X of general type with p g = 0 it suffices to prove that one single point of a transcendence degree 2 in X(ℂ), over the minimal subfield of definition k ⊂ ℂ of X, is rationally equivalent to another single point of a transcendence degree...