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arXiv · 2011.03233

Two families of pro-p groups that are not absolute Galois groups

Claudio Quadrelli
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Abstract

Let $p$ be a prime. We produce two new families of pro-$p$ groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-$p$ groups. Moreover, we show in these families one has one-relator pro-$p$ groups which may not be ruled out as absolute Galois groups employing the quadraticity of Galois cohomology (a consequence of Rost-Voevodsky Theorem), or the vanishing of Massey products in Galois cohomology.

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Claudio Quadrelli. 2020-11-06. Two families of pro-p groups that are not absolute Galois groups. https://doi.org/10.1515/jgth-2020-0186

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