$A_3$-formality for Demushkin groups at odd primes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909997468745728 |
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| author | Pál, Ambrus Quick, Gereon |
| author_facet | Pál, Ambrus Quick, Gereon |
| contents | We study a weak form of formality for differential graded algebras, called $A_3$-formality, for the cohomology of pro-p Demushkin groups at odd primes p. We show that the differential graded $\mathbb{F}_p$-algebras of continuous cochains of Demushkin groups with q-invariant not equal 3 are $A_3$-formal, whereas Demushkin groups with q-invariant 3 are not $A_3$-formal. We prove these results by an explicit computation of the Benson-Krause-Schwede canonical class in Hochschild cohomology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_07551 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $A_3$-formality for Demushkin groups at odd primes Pál, Ambrus Quick, Gereon Group Theory Algebraic Topology K-Theory and Homology Number Theory 20J06, 12G05, 16E40, 18N40, 20E18, 55S30 We study a weak form of formality for differential graded algebras, called $A_3$-formality, for the cohomology of pro-p Demushkin groups at odd primes p. We show that the differential graded $\mathbb{F}_p$-algebras of continuous cochains of Demushkin groups with q-invariant not equal 3 are $A_3$-formal, whereas Demushkin groups with q-invariant 3 are not $A_3$-formal. We prove these results by an explicit computation of the Benson-Krause-Schwede canonical class in Hochschild cohomology. |
| title | $A_3$-formality for Demushkin groups at odd primes |
| topic | Group Theory Algebraic Topology K-Theory and Homology Number Theory 20J06, 12G05, 16E40, 18N40, 20E18, 55S30 |
| url | https://arxiv.org/abs/2601.07551 |