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).
Original language | English |
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Pages (from-to) | 77-90 |
Number of pages | 14 |
Journal | Journal of K-Theory |
Volume | 4 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2009 Aug |
Keywords
- Higher algebraic K-theory
- Milnor K-group
- Motivic cohomology
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology