2007/06/29 by Michael Spieß, Michael Spiess, Takao Yamazaki +2
Mathematics · #12G05 (Secondary) #19D45 (Primary) #19F15 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.KT #msc:12G05 #msc:19D45 #msc:19F15
paper · pdf · doi:10.48550/arxiv.0706.4354
13 pages, The previous version was entitled `A counterexample to a conjecture of Somekawa'
openalex publication_date 2007/06/29 · arxiv created 2007/09/07 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We construct an example of a torus T over a field K for which the Galois symbol K(K; T,T)/n K(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).