Enhanced Koszul properties in Galois cohomology

Abstract

We prove that Galois cohomology satisfies several surprisingly strong versions of Koszul properties, under a well known conjecture, in the finitely generated case. In fact, these versions of Koszulity hold for all finitely generated maximal pro-$p$ quotients of absolute Galois groups which are currently understood. We point out several of these unconditional results which follow from our work. We show how these enhanced versions are preserved under certain natural operations on algebras, generalising several results that were previously established only in the commutative case.

arXiv commentTo appear in Research in the Mathematical Sciences. 35 pages, some misprints corrected, exposition improved

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Cited by in corpus (4)

• Pro-p groups with few relations and Universal Koszulity
• Right-angled Artin groups and enhanced Koszul properties
• Right-angled Artin pro-$p$ groups
• Oriented right-angled Artin pro-$\ell$ groups and maximal pro-$\ell$ Galois groups