The Bloch-Kato Conjecture and Galois Theory

TL;DR

This paper explores the structure of Galois groups of maximal p-extensions of fields, examining their filtrations and connections to the Bloch-Kato conjecture, with a focus on third-degree cases and illustrative examples.

Contribution

It provides new insights into the relations within Galois groups and their link to the Bloch-Kato conjecture, especially in the third degree, supported by examples across all degrees.

Findings

Detailed analysis of Galois group filtrations

Connections established with the Bloch-Kato conjecture

Examples illustrating the theory across degrees

Abstract

We investigate the relations in Galois groups of maximal p-extensions of fields, the structure of their natural filtrations, and their relationship with the Bloch-Kato conjecture proved by Rost and Voevodsky with Weibel's patch. Our main focus is on the third degree, but we provide examples for all degrees.