In the book *3264 and All That* by Eisenbud & Harris, the authors claim that for smooth projective varieties admitting an affine stratification, the algebraic equivalence relation and the rational equivalence relation define the same intersection theory (p. 553). Anyway, they do not give an explicit reference where one can find the proof of this claim. I am looking for such a reference.



Equivalence relations among algebraic cycles
In fact more is true: the cycle class map $CH^\*(X)\rightarrow H^\*(X)$
is an isomorphism. See e.g. Fulton's Intersection theory, Examples 1.9.1 and 19.1.11 (b).


