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.

** 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.
$\square$

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like `$\pi$`

). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (1)

Comment #858 by Bhargav Bhatt on