English

$A_3$-formality for Demushkin groups at odd primes

Group Theory 2026-01-23 v2 Algebraic Topology K-Theory and Homology Number Theory

Abstract

We study a weak form of formality for differential graded algebras, called A3A_3-formality, for the cohomology of pro-p Demushkin groups at odd primes p. We show that the differential graded Fp\mathbb{F}_p-algebras of continuous cochains of Demushkin groups with q-invariant not equal 3 are A3A_3-formal, whereas Demushkin groups with q-invariant 3 are not A3A_3-formal. We prove these results by an explicit computation of the Benson-Krause-Schwede canonical class in Hochschild cohomology.

Cite

@article{arxiv.2601.07551,
  title  = {$A_3$-formality for Demushkin groups at odd primes},
  author = {Ambrus Pál and Gereon Quick},
  journal= {arXiv preprint arXiv:2601.07551},
  year   = {2026}
}

Comments

v2: 46 pages; update of the presentation of prior results in the introduction, references added

R2 v1 2026-07-01T09:00:46.104Z