Karoubi's relative Chern character and Beilinson's regulator
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 4, p. 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.

DOI : https://doi.org/10.24033/asens.2174
Classification:  19F27,  19D55,  14F43,  19E20,  19L10,  55R40,  57R20
Keywords: regulator, relative Chern character, secondary characteristic class, Borel regulator
@article{ASENS_2012_4_45_4_601_0,
     author = {Tamme, Georg},
     title = {Karoubi's relative Chern character and Beilinson's regulator},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 45},
     number = {4},
     year = {2012},
     pages = {601-636},
     doi = {10.24033/asens.2174},
     zbl = {1266.19004},
     mrnumber = {3059242},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2012_4_45_4_601_0}
}
Tamme, Georg. Karoubi's relative Chern character and Beilinson's regulator. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 4, pp. 601-636. doi : 10.24033/asens.2174. http://www.numdam.org/item/ASENS_2012_4_45_4_601_0/

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