In Karl Rubin's book Euler System, he gives a definition of selmer groups as below:
Then he states as in lemma 5.3 on page 12 that the selmer group with upper tag is equal to a first cohomology group with appropiate assumption on A:
However, I fail to understand his proof. I'm wondering how to get through the second equality. What's the connection between $H^{1}(I_{v},A)$ and $H^{1}(K_{\sum},A)$? $I$ is the inertia group. Also, I don't understand the third equality.