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L'invariant de Suslin en caractéristique positive

Part of: Whitehead groups and $K_1$

Published online by Cambridge University Press:  08 June 2010

Tim Wouters
Tim Wouters
Affiliation:
K.U.Leuven, Departement Wiskunde, Celestijnenlaan 200B bus 2400, B-3001 Leuven, Belgique, [email protected]
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Abstract

For a central simple k-algebra A with indk (A) ∈ k×, Suslin defined a cohomological invariant for SK1 (A) [Sus2]. In this text, we generalise his invariant to any central simple k-algebra using a lift from positive characteristic to characteristic 0. To be able to define the invariant, we use Kato's cohomology of logarithmic differentials [Kat1].

Résumé

Pour une k-algèbre simple centrale A d'indice inversible dans k, Suslin a défini un invariant cohomologique de SK1 (A) ‘Sus2’. Dans ce texte, nous généralisons cet invariant à toute k-algèbre simple centrale par un relèvement de la caractéristique positive à la caractéristique 0. Pour pouvoir définir cet invariant, on a besoin des groupes de cohomologie des différentielles logarithmiques de Kato [Kat1].

Keywords

Groupe de Whitehead réduitModules de cyclesInvariants cohomologiques

MSC classification

Secondary: 19B99: None of the above, but in this section
Type
Research Article
Information
Journal of K-Theory , Volume 5 , Issue 3 , June 2010 , pp. 559 - 602
Copyright
Copyright © ISOPP 2010

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