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Tag 041Y

Chapter 65: Descent and Algebraic Spaces > Section 65.10: Descending properties of morphisms in the fpqc topology

Lemma 65.10.15. The property $\mathcal{P}(f) =$''$f$ is an isomorphism'' is fpqc local on the base.

Proof. Combine Lemmas 65.10.6 and 65.10.14. $\square$

    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).

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

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