Lemma 48.22.4. Let $X/A$ with $\omega _ X^\bullet $ and $\omega _ X$ be as in Example 48.22.1. Then

$H^ i(\omega _ X^\bullet ) \not= 0 \Rightarrow i \in \{ -\dim (X), \ldots , 0\} $,

the dimension of the support of $H^ i(\omega _ X^\bullet )$ is at most $-i$,

$\text{Supp}(\omega _ X)$ is the union of the components of dimension $\dim (X)$, and

$\omega _ X$ has property $(S_2)$.

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