Lemma 61.3.4 (096H)—The Stacks project

Processing math: 100%

Table of contents
Part 3: Topics in Scheme Theory
Chapter 61: Pro-étale Cohomology
Section 61.3: Local isomorphisms
Lemma 61.3.4 (cite)

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 61.3.4. Let $A$ be a ring. Let $B \to C$ be an $A$ -algebra homomorphism.

If $A \to B$ and $A \to C$ are local isomorphisms, then $B \to C$ is a local isomorphism.
If $A \to B$ and $A \to C$ identify local rings, then $B \to C$ identifies local rings.

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