# 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?

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