Lemma 52.9.3. In Lemma 52.9.2 if instead of the empty condition (2) we assume

1. if $\mathfrak p \in V(I)$ and $\mathfrak p \not= \mathfrak m$, then $\text{depth}_{A_\mathfrak p}(M_\mathfrak p) + \dim (A/\mathfrak p) > s$,

then the conditions also imply that $H^ i_{J_0}(M)$ is a finite $A$-module for $i \leq s$.

Proof. This is a special case of Lemma 52.8.3. $\square$

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