Remark 52.18.3. Let $Y$ be a Noetherian scheme and let $Z \subset Y$ be a closed subset. By Lemma 52.18.1 we have

We claim that if $Y$ is of finite type over a field, then equality holds. If we ever need this result we will formulate a precise result and prove it here. However, in general if we define $\delta _ Z$ by the right hand side of this inequality, then we don't know if Lemma 52.18.2 remains true.

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