Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam–Liu–Sharifi–Wake–Wang. We prove that the pro-p completion of the right-angled Artin group associated to a chordal simplicial graph is of p-absolute Galois type, and moreover it satisfies a strong version of the Massey vanishing property. Also, we prove that Demushkin groups are of p-absolute Galois type, and that the free pro-p product — and, under certain conditions, the direct product — of two pro-p groups of p-absolute Galois type satisfying the Massey vanishing property, is again a pro-p group of p-absolute Galois type satisfying the Massey vanishing property. Consequently, there is a plethora of pro-p groups of p-absolute Galois type satisfying the Massey vanishing property that do not occur as absolute Galois groups.

Blumer, S., Cassella, A., Quadrelli, C. (2023). Groups of p-absolute Galois type that are not absolute Galois groups. JOURNAL OF PURE AND APPLIED ALGEBRA, 227(4 (April 2023)) [10.1016/j.jpaa.2022.107262].

Groups of p-absolute Galois type that are not absolute Galois groups

Simone Blumer;Alberto Cassella;Claudio Quadrelli
2023

Abstract

Let p be a prime. We study pro-p groups of p-absolute Galois type, as defined by Lam–Liu–Sharifi–Wake–Wang. We prove that the pro-p completion of the right-angled Artin group associated to a chordal simplicial graph is of p-absolute Galois type, and moreover it satisfies a strong version of the Massey vanishing property. Also, we prove that Demushkin groups are of p-absolute Galois type, and that the free pro-p product — and, under certain conditions, the direct product — of two pro-p groups of p-absolute Galois type satisfying the Massey vanishing property, is again a pro-p group of p-absolute Galois type satisfying the Massey vanishing property. Consequently, there is a plethora of pro-p groups of p-absolute Galois type satisfying the Massey vanishing property that do not occur as absolute Galois groups.
Articolo in rivista - Articolo scientifico
Absolute Galois groups; Chordal graphs; Galois cohomology; Massey products; Norm residue theorem; Right-angled Artin groups
English
12-nov-2022
2023
227
4 (April 2023)
107262
none
Blumer, S., Cassella, A., Quadrelli, C. (2023). Groups of p-absolute Galois type that are not absolute Galois groups. JOURNAL OF PURE AND APPLIED ALGEBRA, 227(4 (April 2023)) [10.1016/j.jpaa.2022.107262].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/435319
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