Krull topology

Last updated January 27, 2022

Idea

A special case of the profinite topology.

Definition

Let $K/L$ be Galois, and $G=\text{Gal}(K/L)$.

• The Krull topology on $G$ is the one generated by the local topological base $$\mathcal{B}g=\bigcup{L/F \text{ finite}}{\text{subgroups of }\text{Gal}(K/L)}$$
• In terms of a global base, it is $$\mathcal{B}=\bigcup_{L/F \text{ finite}}{\text{cosets of subgroups of }\text{Gal}(K/L)}$$

Examples

1 (finite groups)