The Stacks project

Remark 37.9.6. A special case of Lemmas 37.9.1, 37.9.2, 37.9.4, and 37.9.5 is where $Y = Y'$. In this case the map $A$ is always zero. The sheaf of Lemma 37.9.4 is just given by the rule

\[ U' \mapsto \{ a' : U' \to Y\text{ over }S\text{ with } a'|_ U = a|_ U\} \]

and we act on this by the sheaf $\mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(a^*\Omega _{Y/S}, \mathcal{C}_{X/X'})$.

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