Karoubi's relative Chern character and Beilinson's regulator

Tamme, Georg

Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 4, pp. 601-636.

We construct a variant of Karoubi’s relative Chern character for smooth varieties over $𝐂$ 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.

Nous construisons une variante du caractère de Chern relatif de Karoubi pour les variétés lisses sur $𝐂$ 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.

Classification: 19F27, 19D55, 14F43, 19E20, 19L10, 55R40, 57R20
Keywords: regulator, relative Chern character, secondary characteristic class, Borel regulator
Mot clés : régulateur, caractère de Chern relatif, classe caractéristique secondaire, régulateur de Borel

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