Massey products and unipotent extensions with restricted ramification

TL;DR

This paper constructs new pro-p extensions of number fields with controlled ramification, demonstrating they satisfy the Massey vanishing property and have large unipotent quotients, advancing understanding of Galois groups in number theory.

Contribution

It introduces novel pro-p extensions with restricted ramification that decompose into coproducts of local Galois groups, showing they satisfy Massey vanishing and possess large unipotent quotients.

Findings

Extensions satisfy strong Massey vanishing property

Galois groups decompose as coproducts of local Galois groups

Extensions admit large unipotent quotients

Abstract

We fix a prime p and construct new cases of pro-p extensions of number fields with restricted ramification and splitting, whose Galois groups decompose as coproducts of pro-p absolute Galois groups of local fields. As a consequence, these pro-p extensions satisfy the strong Massey vanishing property and thus admit large unipotent quotients.