The Stacks Project

Tag 041Y

Chapter 62: Descent and Algebraic Spaces > Section 62.10: Descending properties of morphisms in the fpqc topology

Lemma 62.10.15. The property $\mathcal{P}(f) =$''$f$ is an isomorphism'' is fpqc local on the base.

Proof. Combine Lemmas 62.10.6 and 62.10.14. $\square$

    The code snippet corresponding to this tag is a part of the file spaces-descent.tex and is located in lines 1391–1395 (see updates for more information).

    The property $\mathcal{P}(f) =$``$f$ is an isomorphism''
    is fpqc local on the base.
    Combine Lemmas \ref{lemma-descending-property-surjective}
    and \ref{lemma-descending-property-open-immersion}.

    Comments (0)

    There are no comments yet for this tag.

    Add a comment on tag 041Y

    Your email address will not be published.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 lower-right corner).

    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 box. So in case this where tag 0321 you just have to write 0321. Beware of the difference between the letter 'O' and the digit 0.

    This captcha seems more appropriate than the usual illegible gibberish, right?