Karoubi's relative Chern character and Beilinson's regulator

[Le caractère de Chern relatif de Karoubi et le régulateur de Beilinson]

Tamme, Georg

Annales scientifiques de l'École Normale Supérieure, Tome 45 (2012), p. 601-636 / Harvested from Numdam

Résumé

Nous construisons une variante du caractère de Chern relatif de Karoubi pour les variétés lisses sur $\mathbf {C}$ et prouvons un résultat de comparaison avec le régulateur de Beilinson à valeurs dans la cohomologie de Deligne-Beilinson. En corollaire, nous obtenons une nouvelle preuve du théorème de Burgos que, pour un corps de nombres, le régulateur de Beilinson est deux fois le régulateur de Borel.

Abstract

We construct a variant of Karoubi’s relative Chern character for smooth varieties over $\mathbf {C}$ and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.

Détail

Publié le : 2012-01-01

MR 3059242 | Zbl 1266.19004

DOI : https://doi.org/10.24033/asens.2174
Classification:  19F27,  19D55,  14F43,  19E20,  19L10,  55R40,  57R20
Mots clés: régulateur, caractère de Chern relatif, classe caractéristique secondaire, régulateur de Borel

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