Karoubi's relative Chern character and Beilinson's regulator

Tamme, Georg

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

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.

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.

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