et $K$ be a number field and $G_K$ be a absolute Galois group of $K$.
Let $f:N \to M$ be an injetion of map between $G_K$modules.
Then, induced map $f^*$ between Galois Cohomology, $f^*:H^1(G_K,N)\to H^1(G_K,M)$ is not necessalily injective.
What kind of condition on $f$ implies $f^*$ is also injetive ?
For example, if $f$ is inclusion as a set, is $f^*$ injection ?
P.S.
Thanks to Mathmo123, I heard $Kerf^* \cong \frac{(M/N)^{G_K}}{M^{G_K}/N^{G_K}}$ still I don't understand why this holds.
I don't understand why this isomorphism holds. Short exact sequence $0 \to N \to M \to M/N \to 0$ induces long exact sequence $0 \to N \to M \to M/N \to H^1(G_K,N) \to H^1(G_K,M)\to・・・$.