I'm learning p-adic Galois representation, here is the background:
Let $K$ be a p-adic field, and $G_K$ is the absolute Galois group of $K$. Let $V$ be a finite-dimensional p-adic representation of $G_K$. I want to learn the local Euler characteristic about representations. That's something like $$\chi(V)=dim_{\mathbb Q_p}H^0_{cont}(G_K,V)-dim_{\mathbb Q_p} H^1_{cont}(G_K,V)+dim _{\mathbb Q_p}H^2_{cont}(G_K,V)$$ Which may have properties like $\chi(V)$ only depends on the dimension of $V$.
Could you provide some references?