Two families of pro-p groups that are not absolute Galois groups
Number Theory
2021-07-13 v3 Group Theory
Abstract
Let be a prime. We produce two new families of pro- groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro- groups. Moreover, we show in these families one has one-relator pro- 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.
Keywords
Cite
@article{arxiv.2011.03233,
title = {Two families of pro-p groups that are not absolute Galois groups},
author = {Claudio Quadrelli},
journal= {arXiv preprint arXiv:2011.03233},
year = {2021}
}