The kernel unipotent conjecture and the vanishing of Massey products for odd rigid fields

DOI10.1016/J.AIM.2014.12.028zbMATH Open1334.12005arXiv1312.2655OpenAlexW2964024929WikidataQ123251640 ScholiaQ123251640MaRDI QIDQ2253797

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Publication date: 13 February 2015

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Abstract: A major difficult problem in Galois theory is the characterization of profinite groups which are realizable as absolute Galois groups of fields. Recently the Kernel $n$-Unipotent Conjecture and the Vanishing $n$-Massey Conjecture for $ngeq3$ were formulated. These conjectures evolved in the last forty years as a byproduct of the application of topological methods to Galois cohomology. We show that both of these conjectures are true for odd rigid fields. This is the first case of a significant family of fields where both of the conjectures are verified besides fields whose Galois groups of $p$-maximal extensions are free pro-$p$-groups. We also prove the Kernel Unipotent Conjecture for Demushkin groups of rank 2, and establish a number of further related results.

Full work available at URL: https://arxiv.org/abs/1312.2655

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