Approximating Absolute Galois Groups

TL;DR

This paper introduces a new group condition characterizing absolute Galois groups, enabling their approximation by inverse limits of Bieberbach-like groups, which advances the understanding of descent problems in algebraic K-theory.

Contribution

It formulates a novel condition for absolute Galois groups and demonstrates their approximation by profinite Bieberbach analogues, aiding algebraic K-theory studies.

Findings

Absolute Galois groups satisfy the new group condition.

Groups meeting the condition can be approximated by inverse limits of Bieberbach-like groups.

The condition is crucial for the 'representational assembly' approach in descent problems.

Abstract

This paper formulates a group condition which is enjoyed by absolute Galois groups, and which guarantees that profinite groups satisfying the condition can be approximated as an inverse limit of groups which are profinite analogues of Bieberbach groups. The condition is a key ingredient in the study of the "representational assembly" approach to descent problems in algebraic K-theory.