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Norm index formula for the Tate kernels and applications

Published online by Cambridge University Press:  24 May 2011

J. Assim  and
A. Movahhedi
J. Assim
Affiliation:
Université Moulay Ismail, Mathématiques et informatique, B.P 11201 Zitoune Meknès, Meknès 50000, Marocassim@fs-umi.ac.ma
A. Movahhedi
Affiliation:
XLIM UMR 6172 CNRS/Univ. de Limoges, Mathématiques et informatique, 123, Avenue A. Thomas, 87060 Limoges, Francemova@unilim.fr
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Abstract

Let p be an odd prime and L/F a p-extension of number fields with Galois group G. The aim of this paper is to provide answers to a question of Kahn concerning lower bounds for the order of the kernel and cokernel of the functorial map K2F → K2LG. To this end, we first determine a norm index formula for generalized Tate kernels and then express our lower bounds in terms of the ramification in L/F.

Keywords

CapitulationTate kernelIwasawa theoryK-groupCohomology

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Type
Research Article
Information
Journal of K-Theory , Volume 9 , Issue 2 , April 2012 , pp. 359 - 383
Copyright
Copyright © ISOPP 2011

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