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A counterexample to generalizations of the Milnor-Bloch-Kato conjecture

Published online by Cambridge University Press:  25 August 2009

Michael Spiess  and
Takao Yamazaki
Michael Spiess
Affiliation:
Fakultät für Mathematik, Postfach 100131, D-33501 Bielefeld, Germany, mspiess@math.uni-bielefeld.de.
Takao Yamazaki
Affiliation:
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan, ytakao@math.tohoku.ac.jp.
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Abstract

We construct an example of a torus T over a field K for which the Galois symbol K(K;T,T)/nK(K;T,T) → H2(K,T[n] ⊗ T[n]) is not injective for some n. Here K(K;T,T) is the Milnor K-group attached to T introduced by Somekawa. We show also that the motive M(T × T) gives a counterexample to another generalization of the Milnor-Bloch-Kato conjecture (proposed by Beilinson).

Keywords

Motivic cohomologyhigher algebraic K-theoryMilnor K-group
Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 1 , August 2009 , pp. 77 - 90
Copyright
Copyright © ISOPP 2009

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