Lemma 37.13.5 (0D0L)—The Stacks project

Processing math: 100%

Table of contents
Part 2: Schemes
Chapter 37: More on Morphisms
Section 37.13: The naive cotangent complex
Lemma 37.13.5 (cite)

previous lemma
next lemma

numberstags

history
statistics
4 tags refer to this tag

Lemma 37.13.5. Let $f : X \to Y$ be a morphism of schemes. The following are equivalent

$f$ is formally smooth,
$H^{-1}(\mathop{N\! L}\nolimits _{X/Y}) = 0$ and $H^0(\mathop{N\! L}\nolimits _{X/Y}) = \Omega _{X/Y}$ is locally projective.

Proof. This follows from Algebra, Proposition 10.138.8 and Lemma 37.11.10. $\square$

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