The Smoothness Conjecture for profinite groups

Let $G$ be a profinite group. Recall that $G$ is 1-smooth if it satisfies the relevant lifting property for cyclotomic modules. The weak Bloch–Kato property at $p$ means that, for every integer $n\geq 1$ and every open subgroup $H\subset G$, every class in $H^n(H,k)$ is a quasi-symbol relative to the trivial one-dimensional $(k,G)$-module $k$. A profinite group is smooth if it is $1$-smooth for every relevant prime and cyclotomic datum.

Smoothness Conjecture. If $G$ is $1$-smooth, then it has the weak Bloch–Kato property. In particular, it is smooth.

This conjecture connects the lifting-theoretic notion of smoothness with the Bloch–Kato-type description of continuous cohomology by quasi-symbols. The source says that it is intended to be proved in future work; no resolution is supplied here.