Lemma 67.21.1 (03WK)—The Stacks project

Processing math: 100%

Table of contents
Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.21: Quasi-affine morphisms
Lemma 67.21.1 (cite)

next definition

numberstags

history
statistics

Lemma 67.21.1. Let $S$ be a scheme. Let $f : X \to Y$ be a representable morphism of algebraic spaces over $S$ . Then $f$ is quasi-affine (in the sense of Section 67.3) if and only if for all affine schemes $Z$ and morphisms $Z \to Y$ the scheme $X \times _ Y Z$ is quasi-affine.

Proof. This follows directly from the definition of a quasi-affine morphism of schemes (Morphisms, Definition 29.13.1). $\square$

Comments (0)

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).

Comments (0)

Post a comment