Koszul algebras and quadratic duals in Galois cohomology

We investigate the Galois cohomology of finitely generated maximal pro-$p$ quotients absolute groups. Assuming well-known conjectural description these groups, we show that has PBW property. Hence in particular it is a Koszul algebra. This answers positively conjecture by Positselski this case. also provide an analogous unconditional result about Pythagorean fields. Moreover, establish some results relate quadratic dual with $p$-Zassenhaus filtration on group. paper contains survey property and its relation