Syntomic regulators and special values of \(p\)-adic \(L\)-functions
type: Item
instance of: scholarly article
title: Syntomic regulators and special values of \(p\)-adic \(L\)-functions
zbMATH Open document ID: 0910.11046
author: Manfred Kolster
author: Thong Nguyen Quang Do
published in: Inventiones Mathematicae
publication date: 1999-04-08T00:00:00Z
review text: As a generalization of Leopoldt's \(p\)-adic class number formula, the authors prove \(p\)-adic analogs of the Lichtenbaum conjectures for abelian number fields \(F\), which 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, the \(p\)-adic equivalent of the Beilinson regulator maps, which are compared with etale regulators via the Fontaine-Messing map. Computations of Bloch-Kato when \(p\) is unramified in \(F\) lead to results about generalized Coates-Wiles homomorphisms and cyclotomic characters.
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1199918
zbMATH Keywords: abelian number field
zbMATH Keywords: \(p\)-adic number
zbMATH Keywords: special values of \(p\)-adic \(L\)-functions
zbMATH Keywords: Lichtenbaum conjectures
zbMATH Keywords: syntomic regulator
reviewed by: Xianke Zhang
MaRDI profile type: Publication
full work available at URL: s002220050250
OpenAlex ID: W2078727552
DOI: 10.1007/S002220050250
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description: scientific article; zbMATH DE number 1199918