Exercise 5, § 10

Let $I$ be a finite subset of $N$.

a) Construct a regular local ring $B$ and a $B$-module $N$ such that the set of integers $p$ such that $H_B^p(N) \neq 0$ is equal to $I$ (consider a direct sum).

b) Construct a local ring $A$ such that the set of integers $p$ such that $H_A^p(A) \neq 0$ is equal to $I$ (take $A = B \oplus N$, where $N$ is a square zero ideal, and use Exercise 3).