English

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

Number Theory 2021-07-13 v3 Group Theory

Abstract

Let pp be a prime. We produce two new families of pro-pp groups which are not realizable as absolute Galois groups of fields. To prove this we use the 1-smoothness property of absolute Galois pro-pp groups. Moreover, we show in these families one has one-relator pro-pp 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}
}