The Stacks project

[Expose X, Proposition 1.2, p. 262, SGA1].

Lemma 58.15.1. Let $f : X \to S$ be a proper morphism of schemes. Let $X \to S' \to S$ be the Stein factorization of $f$, see More on Morphisms, Theorem 37.53.5. If $f$ is of finite presentation, flat, with geometrically reduced fibres, then $S' \to S$ is finite étale.

Proof. This follows from Derived Categories of Schemes, Lemma 36.32.8 and the information contained in More on Morphisms, Theorem 37.53.5. $\square$


Comments (0)

There are also:

  • 2 comment(s) on Section 58.15: Homotopy exact sequence

Post a comment

Your email address will not be published.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.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0BUN. Beware of the difference between the letter 'O' and the digit '0'.