Bloch–Kato norm residue conjecture

Let $k$ be a field of characteristic different from a prime number $p$. For each nonnegative integer $n$, let $K_n^M(k)/(p)$ denote Milnor $K$-theory modulo $p$, and let $\mu_p^{\otimes n}$ denote the $n$-fold tensor power of the étale sheaf of $p$th roots of unity. The norm residue homomorphism is

$$N\colon K_n^M(k)/(p)\ifnextchar/{\toop}{\toop/>/} \mathbb{H}_{\operatorname{et}}^n(\operatorname{Spec} k,\mu_p^{\otimes n}).$$

Bloch–Kato conjecture. This norm residue homomorphism is an isomorphism for any nonnegative integer $n$.

This is the Bloch–Kato conjecture, also called the Milnor conjecture at the prime $p=2$, and it is the central norm-residue statement motivating the manuscript. Its resolution is not established in the supplied source context.