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19-XX $K$ -theory
19Fxx $K$ -theory in number theory

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Karoubi’s relative Chern character and Beilinson’s regulator

Georg Tamme (2012)

Annales scientifiques de l'École Normale Supérieure

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.

K-groups and ideal class groups of number fields.

Keiichi Komatsu (1991)

Manuscripta mathematica

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