A counterexample to generalizations of the Milnor - Bloch - Kato
نویسنده
چکیده
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 ) → H(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-BlochKato conjecture (proposed by Beilinson).
منابع مشابه
S ep 2 00 7 A counterexample to generalizations of the Milnor - Bloch - Kato conjecture ∗
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 ) → H(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 motiveM(T×T ) gives a counterexample to another generalization of the Milnor-BlochKato conjecture (proposed by Beilinson).
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