The Stacks project

35.29 Properties of morphisms local in the syntomic topology on the source

Here are some properties of morphisms that are syntomic local on the source.

Lemma 35.29.1. The property $\mathcal{P}(f)=$“$f$ is syntomic” is syntomic local on the source.

Proof. Combine Lemma 35.26.4 with Morphisms, Lemma 29.30.2 (local for Zariski on source and target), Morphisms, Lemma 29.30.3 (pre-composing), and Lemma 35.14.4 (part (4)). $\square$

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