The syntomic regulator for the K-theory of fields

Besser, A.; de Jeu, R.

Abstract

We define complexes analogous to Goncharov's complexes for the K-theory of discrete valuation rings of characteristic zero. Under suitable assumptions in K-theory, there is a map from the cohomology of those complexes to the K-theory of the ring under consideration. In case the ring is a localization of the ring of integers in a number field, there are no assumptions necessary. We compute the composition of our map to the K-theory with the syntomic regulator. The result can be described in terms of a p-adic polylogarithm. Finally, we apply our theory in order to compute the regulator to syntomic cohomology on Beilinson's cyclotomic elements. The result is again given by the p-adic polylogarithm. This last result is related to one by Somekawa and generalizes work by Gros.

Citation

Besser, A., & de Jeu, R. (2003). The syntomic regulator for the K-theory of fields. Annales Scientifiques de l’École Normale Supérieure, 36(6), 867-924. https://doi.org/10.1016/j.ansens.2003.01.003

• Journal Article Type: Article
• Publication Date: Nov 1, 2003
• Deposit Date: May 1, 2007
• Journal: Annales Scientifiques de l'École normale supérieure.
• Print ISSN: 0012-9593
• Publisher: Société Mathematique de France
• Peer Reviewed: Peer Reviewed
• Volume: 36
• Issue: 6
• Pages: 867-924
• DOI: https://doi.org/10.1016/j.ansens.2003.01.003
• Public URL: https://durham-repository.worktribe.com/output/1598726