Exercise 5, § 1

Let $A$ be a noetherian ring, $M$ a nonzero finitely generated $A$-module, $J$ an ideal of $A$, $x = (x_1, \ldots, x_n)$ a generator system of $J$. Prove that one has $H^i(x, M) \neq 0$ for $\mathrm{prof}_A(J; M) \leq i \leq n$ (reduce to the local case, and use A, X, p. 157, Cor. 2).