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A p-adic analogue of the Borel regulator and the Bloch–Kato exponential map

Part of: $K$-theory in number theory Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  05 August 2010

Annette Huber  and
Guido Kings
Annette Huber
Affiliation:
Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstrasse 1, 79104 Freiburg im Breisgau, Germany ([email protected])
Guido Kings
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Universitätsstrasse 31, 93053 Regensburg, Germany ([email protected])
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Abstract

In this paper we define a p-adic analogue of the Borel regulator for the K-theory of p-adic fields. The van Est isomorphism in the construction of the classical Borel regulator is replaced by the Lazard isomorphism. The main result relates this p-adic regulator to the Bloch–Kato exponential and the Soulé regulator. On the way we give a new description of the Lazard isomorphism for certain formal groups. We also show that the Soulé regulator is induced by continuous and even analytic classes.

Keywords

p-adic regulatorBorel regulatorsyntomic cohomologycontinuous group cohomologyLie algebra cohomologyLazard isomorphism

MSC classification

Secondary: 11S70: $K$-theory of local fields 19F27: Étale cohomology, higher regulators, zeta and $L$-functions
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 10 , Issue 1 , January 2011 , pp. 149 - 190
Copyright
Copyright © Cambridge University Press 2010

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