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

Michael Spiess, Takao Yamazaki

We construct an example of a torus $T$ over a field $K$ for which the Galois symbol $K(K;T,T)/nK(K;T,T)\to H^2(K,T[n]\otimes T[n])$ is not injective for some $n$. Here $K(K; T…