Lemma 62.6.2 (0H51)—The Stacks project

Loading web-font TeX/Math/Italic

Table of contents
Part 3: Topics in Scheme Theory
Chapter 62: Relative Cycles
Section 62.6: Relative cycles
Lemma 62.6.2 (cite)

previous definition
next lemma

numberstags

history
statistics
3 tags refer to this tag

Lemma 62.6.2. Let $\alpha$ be a relative $r$ -cycle on $X/S$ as in Definition 62.6.1. Then any restriction, base change, flat pullback, or proper pushforward of $\alpha$ is a relative $r$ -cycle.

Proof. For flat pullback use Lemma 62.4.4. Restriction is a special case of flat pullback. To see it holds for base change use that base change is transitive. For proper pushforward use Lemma 62.4.5. $\square$

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