Digraphs, pro-p groups and Massey products in Galois cohomology

2024/03/03 by Quadrelli, Claudio
#12F10 #20F36 #20J06 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #Primary 12G05 #Secondary 20E18

paper · doi:10.48550/arxiv.2403.01464

Abstract

Let p be a prime. We characterize the oriented right-angled Artin pro-p groups whose \mathbbF_p-cohomology algebra yields no essential n-fold Massey products for every n>2, in terms of the associated digraph. Moreover, we show that the \mathbbF_p-cohomology algebra of such oriented right-angled Artin pro-p groups is isomorphic to the exterior Stanley-Reisner \mathbbF_p-algebra associated to the same digraph. This work also aims at providing a concrete and group-theoretic introduction to the study of Massey products in Galois cohomology for non-specialists, especially graduate students working in profinite group theory.

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