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Can somone provide me (articles/literature) with examples of Chow rings of surfaces?

(e.g. here: Chapter 9)

What I want is a list of (smooth projective surface $X/\mathbf{F}_q$, $CH^*(X)=CH^0(X)⊕CH^1(X)⊕CH^2(X)$, the product structure on this, $\mathrm{deg}: CH^2(X) \to \mathbf{Z}$ and the ample cone).

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1 Answer 1

For rational surfaces, there is the paper by Colliot-Thélène Hilbert's Theorem 90 for K2, with Application to the Chow Groups of Rational Surfaces.

For K3 surfaces, there is the paper by Beauville and Voisin On the Chow ring of a K3 surface.

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