Lemma 45.8.2 (0FH6)—The Stacks project

Processing math: 100%

Table of contents
Part 3: Topics in Scheme Theory
Chapter 45: Weil Cohomology Theories
Section 45.8: Cycles over non-closed fields
Lemma 45.8.2 (cite)

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 45.8.2. Let $K/k$ be an algebraic field extension. Let $X$ be a finite type scheme over $k$ . Then $\mathop{\mathrm{CH}}\nolimits _ i(X_ K) = \mathop{\mathrm{colim}}\nolimits \mathop{\mathrm{CH}}\nolimits _ i(X_{k'})$ where the colimit is over the subextensions $K/k'/k$ with $k'/k$ finite.

Proof. This is a special case of Chow Homology, Lemma 42.67.10. $\square$

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