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 42.66.10.
$\square$

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