Pro-$p$ groups with few relations and universal Koszulity - Quadrelli, Claudio (Mathematica Scandinavica, 2021)
Let $p$ be a prime. We show that if a pro-$p$ group with at most $2$ defining relations has quadratic $\mathbb{F}_p$-cohomology algebra, then this algebra is universally Koszul. This proves the “Universal Koszulity Conjecture” formulated by J. Mináč et al. in the case of maximal pro-$p$ Galois groups of fields with at most $2$ defining relations.