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Aug 16, 2020 at 3:41 comment added abx For $X$ a smooth projective curve of genus $\geq 1$ defined over $\mathbb{Q}$, $CH^1(X)=\operatorname{Pic}(X) $ is finitely generated, while $CH^1(X\otimes _{\mathbb{Q}}\mathbb{C})$ is an extension of $\mathbb{Z} $ by a complex torus.
Aug 15, 2020 at 22:47 history edited curious math guy CC BY-SA 4.0
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Aug 15, 2020 at 21:52 comment added R. van Dobben de Bruyn Note that $X \amalg X$ is already a covering of $X$ in the (big) Zariski site. Somehow the objects that appear in the site and the families that form coverings are separate (unrelated) notions. This question is only about objects and does not see the Grothendieck (pre)topology.
Aug 15, 2020 at 20:26 history asked curious math guy CC BY-SA 4.0