Koszul property and Bogomolov's conjecture

TL;DR

This paper extends Bogomolov's conjecture to all fields, linking it with Milnor K-theory and homological properties, and discusses the implications for Galois groups and related algebraic structures.

Contribution

It introduces a generalized form of Bogomolov's conjecture applicable to any field and connects it with Milnor K-theory and homological algebra.

Findings

A weaker conjecture is derived from the main hypothesis.

The Milnor-Bloch-Kato conjecture is shown to follow from the same hypothesis.

The paper discusses the homological properties of Milnor K-theory algebras.

Abstract

This is an enhanced version of the author's 1998 Harvard Ph.D. thesis, as published by IMRN in 2005. We propose an extension of Bogomolov's conjecture about commutator subgroups of Galois groups to arbitrary fields. A somewhat weaker conjecture is then shown to follow, together with the famous Milnor-Bloch-Kato conjecture, from a certain hypothesis about homological properties of the Milnor K-theory algebras.