Universal Koszulity conjecture for Galois cohomology

Let $p$ be prime, let $F$ be a field containing a primitive $p$th root of unity, and assume that $G_F(p)$ is finitely generated. Write $H^\bullet(G_F(p),\mathbb{F}_p)$ for the continuous cohomology algebra. An algebra is universally Koszul when every ideal generated by degree-$1$ elements, equivalently every cyclic module of the relevant form, has a linear resolution. Universal Koszulity conjecture. The algebra

$$H^\bullet(G_F(p),\mathbb{F}_p)$$

is universally Koszul. The paper presents this as a strengthening of the quadraticity supplied by Bloch–Kato; it is proved conditionally under the Elementary Type Conjecture, while the unconditional general case remains open.