Inventiones mathematicae

, Volume 133, Issue 2, pp 417–447

Syntomic regulators and special values of p-adic L-functions

  • Manfred Kolster
  • Thong Nguyen Quang Do

DOI: 10.1007/s002220050250

Cite this article as:
Kolster, M. & Do, T. Invent math (1998) 133: 417. doi:10.1007/s002220050250


In this paper p-adic analogs of the Lichtenbaum Conjectures are proven for abelian number fields F and odd prime numbers p, which generalize Leopoldt's p-adic class number formula, and express special values of p-adic L-functions in terms of orders of K-groups and higher p-adic regulators. The approach uses syntomic regulator maps, which are the p-adic equivalent of the Beilinson regulator maps. They can be compared with étale regulators via the Fontaine-Messing map, and computations of Bloch-Kato in the case that p is unramified in F lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Manfred Kolster
    • 1
  • Thong Nguyen Quang Do
    • 2
  1. 1. McMaster University, Department of Mathematics, 1250 Main Street West, Hamilton, Ontario L8S 4K1, CanadaCA
  2. 2. Université de Franche-Comté, Laboratoire de Mathématiques, 16, Route de Gray, F-25030 Besancon Cedex, FranceFR