Let $M[p] = (m \in M: pm = 0) \subset M$, where $M$ is an abelian group. I have shown that the assignment $F(M) = M[p]$ is a left exact functor. How would I determine what the right derived functors are?
To my understanding, we want to continue the exact sequence $0 \to F(M') \to F(M) \to F(M'')$ on the right. To do so, we want the image of $F(M)$ to be mapped to $0$ in $(R_1F)(M')$.