The Elementary Type Conjecture for Maximal Pro-p Galois groups

The Elementary Type Conjecture in Galois theory provides a concrete inductive description of the finitely generated maximal pro-p Galois groups GF(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.