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• W3173118097 abstract "Let $p$ be a prime. A cohomologically Kummerian oriented pro-$p$ group is a pair consisting of a pro-$p$ group $G$ together with a continuous $G$-module $mathbb{Z}_p(theta)$ isomorphic to $mathbb{Z}_p$ as an abelian pro-$p$ group, such that the natural map in cohomology $H^1(G,mathbb{Z}_p(theta)/p^n)to H^1(G,mathbb{Z}_p(theta)/p)$ is surjective for every $ngeq1$. One has a 1-cyclotomic oriented pro-$p$ group if cohomological Kummerianity holds for every closed subgroup. By Kummer theory, the maximal pro-$p$ Galois group of a field containing a root of 1 of order $p$ together with the cyclotomic character is 1-cyclotomic. We prove that cohomological Kummerianity is preserved by certain quotients of pro-$p$ groups, and we extend the group-theoretic characterization of cohomologically Kummerian oriented pro-$p$ groups, established by I.~Efrat and the author, to the non-finitely generated case. We employ these results to find interesting new examples of pro-$p$ groups which do not occur as absolute Galois groups, which other methods fail to detect." @default.
• W3173118097 created "2021-06-22" @default.
• W3173118097 creator A5086678712 @default.
• W3173118097 date "2021-06-01" @default.
• W3173118097 modified "2023-09-27" @default.
• W3173118097 title "Chasing maximal pro-p Galois groups with 1-cyclotomicity" @default.
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• W3173118097 hasPublicationYear "2021" @default.
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