A non-commutative tensor square of $\mathbb Z$ and the Riemann Hypothesis

For effective applications of the absolute geometry in arithmetic we need a nontrivial absolute tensor square of $\mathbb Z$. However all the known constructions lead to trivial squares. To improve the situation one may try to use a non-commutative tensor square instead. But there is no consideration to imitate in this case. In the talk we are going to present a relation between the RH and an $NC$-tensor product.