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I have trouble understanding "bivariant Chow groups". Remember that for any morphism of schemes $f:X\rightarrow Y$, we can define a bivariant Chow group $A^*(f:X\rightarrow Y)$. When $Y$ is a point, it is just the usual Chow groups $A^*(X)$.

I came cross with this when I was reading a paper and took a look at Fulton's Intersection Theory, but I cannot really understand what he is doing there. Could anyone explain what bivariant Chow group is intuitively?

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