Definition 107.19.2. Let $f : X \to S$ be a family of curves with Cohen-Macaulay fibres equidimensional of dimension $1$ (Lemma 107.8.2). Then the $\mathcal{O}_ X$-module

\[ \omega _{X/S} = H^{-1}(\omega _{X/S}^\bullet ) \]

studied in Lemma 107.19.1 is called the *relative dualizing sheaf* of $f$.

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