Lemma 76.48.6 (06C9)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.48: Local complete intersection morphisms
Lemma 76.48.6 (cite)

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Syntomic equals flat plus lci (for algebraic spaces).

Lemma 76.48.6. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ . The following are equivalent

$f$ is flat and a local complete intersection morphism, and
$f$ is syntomic.

Proof. Omitted. Hint: Use the schemes version of this lemma, see More on Morphisms, Lemma 37.62.8. $\square$

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Comment #858 by Bhargav Bhatt on July 26, 2014 at 16:24

Suggested slogan: Syntomic equals flat plus lci (for algebraic spaces).

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