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The Stacks project

Lemma 76.17.5. Same notation and assumptions as in Lemma 76.17.4. We identify sheaves on X and X' via (76.9.1.1). There is an action of the sheaf

\mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(a^*\Omega _{Y/B}, \mathcal{C}_{X/X'})

on the sheaf (76.17.4.1). Moreover, the action is simply transitive for any object U' of (X')_{spaces, {\acute{e}tale}} over which the sheaf (76.17.4.1) has a section.


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