# 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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