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algebraic quantity principle – Galois invariants of group cohomology Answer

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algebraic quantity principle – Galois invariants of group cohomology

Suppose $G$ is a few (abelian, plane) group and $M/mathbb Q$ is a vector area with a $G$ motion and a submodule $N$. I’ve an component $X$ in $H^1(G,Motimes_{mathbb Q}overline{mathbb Q})$ that’s steady underneath the Galois motion of $Gamma = mathrm{Gal}(overline{mathbb Q}/mathbb Q)$ and furthermore, it lies within the picture of the map $H^1(G,Notimes_{mathbb Q}overline{mathbb Q}) to H^1(G,Notimes_{mathbb Q}overline{mathbb Q})$. Does this indicate that $X$ actually comes from an component in $H^1(G,N)$?

I cerebrate this could breathe some dispute moving the Hotschild-Serre spectral sequence however I am unable to fairly labor it out.

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