Compact Galois module
= Compact Galois module
A compact Galois module is a compact <profinite abelian group> equipped with a continuous <Galois group> action. An abelian <pro-p group> is naturally a compact $\mathbb Z_p$-<module>. A continuous action of the <Galois group> of a <Zp-extension> extends to its <Iwasawa algebra of a Zp-extension>. This compact topology differs from the discrete topology usually used in <Galois cohomology>.