Galois Cohomology (doubt in greenberg's paper)

by math   Last Updated October 10, 2019 02:20 AM - source

I'm reading the paper "Iwasawa Theory for p-adic representation" in which I am not unable to follow one statement:

Let $K \subset \overline {\mathbb Q} $ be a finite extension of $\mathbb Q$. Let $V_p$ be a representation space over $\mathbb Q_p$ for $G_K=Gal(\overline K/K)$ of dimension d, $T_p$ a $G_K$-invariant lattice, and $A=V_P/T_p \cong (\mathbb Q_p/\mathbb Z_p)^d.$ Let $Ram(V_p)$ denote the set of places of $K$ which are unramified in $K(A)/K$. Assume that $Ram(V_p)$ is finite. Let $S$ be a finite set of places of $K$ containing $Ram(V_p)$, all places over $p$, and all infinite places. Let $K_s$ denote the maximal extension of $K$ unramified outside $S$.

Question: Why A is a $Gal(K_S/K)$ module?

Related Questions

Hilbert 90 and K-forms

Updated April 12, 2018 10:20 AM

What is the Weil group of a global field $K$?

Updated October 14, 2017 17:20 PM

Aritn-Schreier tower

Updated August 05, 2019 14:20 PM