The Stacks project

Lemma 15.100.3. Let $A$ be a Noetherian ring. Let $I \subset A$ be an ideal. Let $M$, $N$ be $A$-modules with $M$ finite and $N$ annihilated by a power of $I$. For each $p > 0$ there exists an $n$ such that the map $\mathop{\mathrm{Ext}}\nolimits _ A^ p(M, N) \to \mathop{\mathrm{Ext}}\nolimits _ A^ p(I^ nM, N)$ is zero.

Proof. Immediate consequence of Lemma 15.100.2 and the fact that $I^ mN = 0$ for some $m > 0$. $\square$


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