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Generalized Beilinson Elements and Generalized Soulé Characters

Part of: Curves Arithmetic algebraic geometry

Published online by Cambridge University Press:  06 February 2020

Kenji Sakugawa
Kenji Sakugawa*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 6068502, Japan Email: sakugawa@kurims.kyoto-u.ac.jp
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Abstract

The generalized Soulé character was introduced by H. Nakamura and Z. Wojtkowiak and is a generalization of Soulé’s cyclotomic character. In this paper, we prove that certain linear sums of generalized Soulé characters essentially coincide with the image of generalized Beilinson elements in K-groups under Soulé’s higher regulator maps. This result generalizes Huber–Wildeshaus’ theorem, which is a cyclotomic field case of our results, to an arbitrary number fields.

Keywords

generalized Beilinson elementgeneralized Soulé characterpolylogarithm

MSC classification

Primary: 11G55: Polylogarithms and relations with $K$-theory
Secondary: 14H45: Special curves and curves of low genus
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 2 , April 2021 , pp. 542 - 571
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Copyright
© Canadian Mathematical Society 2020

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