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Special correspondences and Chow traces of Landweber-Novikov operations

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Special correspondences and Chow traces of Landweber-Novikov operations

Auteurs : K. Zainoulline [Allemagne]

Source :

Journal für die reine und angewandte Mathematik (Crelles Journal) [ 0075-4102 ] ; 2009-03.

RBID : ISTEX:A65CF7DE198B7E5C481B72B40F2EF6D690156DDC

English descriptors

KwdEn :
- Algebraic, Algebraic cobordism, Canonical morphism, Cartan formulas, Cellular variety, Certain operations, Chow, Chow group, Chow motive, Chow ring, Chow traces, Cobordism, Commutative diagram, Crucial role, Degree coprime, Dimension reasons, Direct computations, Generalised degree formula, Irreducible variety, Last summand, Lazard ring, Main result, Motivic decomposition, Positive dimension, Positive dimensions, Present section, Previous section, Reine angew, Rost, Rost number, Smooth variety, Special correspondence, Splitting variety, Summand, Symmetric operations, Tangent bundle, Zainoulline.
Teeft :
- Algebraic, Algebraic cobordism, Canonical morphism, Cartan formulas, Cellular variety, Certain operations, Chow, Chow group, Chow motive, Chow ring, Chow traces, Cobordism, Commutative diagram, Crucial role, Degree coprime, Dimension reasons, Direct computations, Generalised degree formula, Irreducible variety, Last summand, Lazard ring, Main result, Motivic decomposition, Positive dimension, Positive dimensions, Present section, Previous section, Reine angew, Rost, Rost number, Smooth variety, Special correspondence, Splitting variety, Summand, Symmetric operations, Tangent bundle, Zainoulline.

Abstract

We prove that the function field of a variety which possesses a special correspondence in the sense of M. Rost preserves rationality of cycles of small codimensions. This fact was proven by Vishik in the case of quadrics and played the crucial role in his construction of fields with u-invariant 2 r + 1. The main technical tools are the algebraic cobordism of Levine-Morel, the generalised degree formula and the divisibility of Chow traces of certain Landweber-Novikov operations. As a direct application of our methods we prove the similar fact for all F 4-varieties.

Url:

https://api.istex.fr/document/A65CF7DE198B7E5C481B72B40F2EF6D690156DDC/fulltext/pdf

DOI: 10.1515/CRELLE.2009.023

Affiliations:

Allemagne

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Le document en format XML

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<front><div type="abstract" xml:lang="en">We prove that the function field of a variety which possesses a special correspondence in the sense of M. Rost preserves rationality of cycles of small codimensions. This fact was proven by Vishik in the case of quadrics and played the crucial role in his construction of fields with u-invariant 2 r + 1. The main technical tools are the algebraic cobordism of Levine-Morel, the generalised degree formula and the divisibility of Chow traces of certain Landweber-Novikov operations. As a direct application of our methods we prove the similar fact for all F 4-varieties.</div>
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Special correspondences and Chow traces of Landweber-Novikov operations

Special correspondences and Chow traces of Landweber-Novikov operations

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English descriptors

Abstract

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