Exercise 111.43.8. Let $A$ be a ring. Let $I = (f_1, \ldots , f_ t)$ be a finitely generated ideal of $A$. Let $U \subset \mathop{\mathrm{Spec}}(A)$ be the complement of $V(I)$. Given a quasi-coherent $\mathcal{O}_{\mathop{\mathrm{Spec}}(A)}$-module $\mathcal{F}$ and $\xi \in H^ p(U, \mathcal{F})$ with $p > 0$, show that there exists $n > 0$ such that $f_ i^ n \xi = 0$ for $i = 1, \ldots , t$. Hint: One possible way to proceed is to use the complex you found in Exercise 111.43.2.

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