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

Michael Spiess, Takao Yamazaki

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 languageEnglish
Pages (from-to)77-90
Number of pages14
JournalJournal of K-Theory
Issue number1
Publication statusPublished - 2009 Aug


  • Higher algebraic K-theory
  • Milnor K-group
  • Motivic cohomology

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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