Lemma 51.4.5 (0DXA)—The Stacks project

Loading web-font TeX/Math/Italic

Table of contents
Part 3: Topics in Scheme Theory
Chapter 51: Local Cohomology
Section 51.4: Cohomological dimension
Lemma 51.4.5 (cite)

previous lemma
next lemma

numberstags

history
statistics
4 tags refer to this tag

Lemma 51.4.5. Let $A \to B$ be a ring map. Let $I \subset A$ be a finitely generated ideal. Then $\text{cd}(B, IB) \leq \text{cd}(A, I)$ . If $A \to B$ is faithfully flat, then equality holds.

Proof. Use the definition and Dualizing Complexes, Lemma 47.9.3. $\square$

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