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arXiv · 2509.10168

The Elementary Type Conjecture for Maximal Pro-p Galois groups

Ido Efrat
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Abstract

The Elementary Type Conjecture in Galois theory provides a concrete inductive description of the finitely generated maximal pro-$p$ Galois groups $G_F(p)$ of fields $F$ containing a root of unity of order $p$. We describe several variants of this conjecture, and prove various connections between these variants and other conjectures in field and Galois theory. We focus on a strong arithmetical variant of the conjecture, and its implications to the realization of pro-$p$ Demuskin groups as Galois groups.

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Ido Efrat. 2025-09-12. The Elementary Type Conjecture for Maximal Pro-p Galois groups. https://arxiv.org/abs/2509.10168

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