Reference for a result in toric geometry

Question

I want to know where I can find the proof of the following theorem : if $X$ is a smooth toric variety, then $H^{\bullet}(X) \cong CH^{\bullet}(X)$.

Thanks in advance !

Answer 1

In Section 5.2 of Fulton there is a theorem that says that for $X$ a smooth complete toric variety, $CH_*X \cong H_*X$, freely generated by the orbit closures.

Your statement follows by Poincare duality and universal coefficient theorem.