Lemma 87.17.1 (0AJ9)—The Stacks project

Processing math: 100%

Table of contents
Part 5: Topics in Geometry
Chapter 87: Formal Algebraic Spaces
Section 87.17: Quasi-compact formal algebraic spaces
Lemma 87.17.1 (cite)

next definition

numberstags

history
statistics
2 tags refer to this tag

Lemma 87.17.1. Let $S$ be a scheme. Let $X$ be a formal algebraic space over $S$ . The following are equivalent

the reduction of $X$ (Lemma 87.12.1) is a quasi-compact algebraic space,
we can find $\{ X_ i \to X\} _{i \in I}$ as in Definition 87.11.1 with $I$ finite,
there exists a morphism $Y \to X$ representable by algebraic spaces which is étale and surjective and where $Y$ is an affine formal algebraic space.

Proof. Omitted. $\square$

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