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Opérations En K-Théorie Algébrique

Published online by Cambridge University Press:  20 November 2018

Christophe Soulé
Christophe Soulé*
Affiliation:
Université Paris VII, Paris, France
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C'est pour étendre le théorème de Riemann-Roch à un morphisme projectif arbitraire que Grothendieck a introduit le groupe K(X) (noté aujourd'hui K0(X)), construit à l'aide des -modules localement libres sur un schéma X[14]. La somme directe et le produit tensoriel de modules font de K0(X) un anneau, et les opérations de puissances extérieures lui fournissent une structure supplémentaire, que Grothendieck appelle λ-anneau. Un λ-anneau est muni d'une filtration décroissante, la γ-filtration, et un des principaux résultats de Grothendieck est que, si X est lisse sur un corps, le groupe

est isomorphe, à la torsion près, au groupe de Chow CH1(X) des cycles de codimension i sur X, modulo l'équivalence linéaire.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 37 , Issue 3 , 01 June 1985 , pp. 488 - 550
Copyright
Copyright © Canadian Mathematical Society 1985

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