Remark 42.32.3. We will see later (Lemma 42.36.3) that if $X$ is a vector bundle of rank $r$ over $Y$ then the pullback map $\mathop{\mathrm{CH}}\nolimits _ k(Y) \to \mathop{\mathrm{CH}}\nolimits _{k + r}(X)$ is an isomorphism. This is true whenever $X \to Y$ satisfies the assumptions of Lemma 42.32.1, see [Lemma 2.2, Totaro-group]. We will sketch a proof in Remark 42.32.8 using higher chow groups.

## Post a comment

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)