Pro-p groups with few relations and Universal Koszulity

Abstract

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, then such 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.

To appear on "Math. Scandinavica"

References in corpus (3)

• Algebraic invariants for right-angled Artin groups
• Koszul property and Bogomolov's conjecture
• On pro-$p$ groups with quadratic cohomology

Cited by in corpus (3)

• Mild pro-p groups and the Koszulity conjectures
• Two families of pro-p groups that are not absolute Galois groups
• Chasing maximal pro-p Galois groups via 1-cyclotomicity