Absolute Galois groups viewed from small quotients and the Bloch-Kato conjecture

TL;DR

This paper explores the connections between small Galois groups, field arithmetic, the Bloch-Kato conjecture, and maximal pro-p quotients of absolute Galois groups, providing new insights into their interrelations.

Contribution

It offers a novel analysis of how small quotients of Galois groups relate to key conjectures and field arithmetic, advancing understanding of Galois group structures.

Findings

Established new relations between small Galois groups and the Bloch-Kato conjecture

Analyzed the structure of maximal pro-p quotients of absolute Galois groups

Provided insights into the arithmetic properties of fields via Galois group analysis

Abstract

In this paper we concentrate on the relations between the structure of small Galois groups, arithmetic of fields, Bloch-Kato conjecture, and Galois groups of maximal pro-$p$-quotients of absolute Galois groups.