Functoriality
The functoriality of cycles, i.e. flat pullback and proper pushforward defined on the level of groups of algebraic cycles Z*(X) extend to Chow groups and give homomorphism of groups
- and
In fact, gives a ring homomorphism on the entire Chow ring (meaning it respects the intersection product, which is clear at least on the set-theoretic level), but does not (since it fails even on the set-theoretic level: we do not always have ). However, we get the so-called projection formula: for Y a subvariety of X and Y′ a subvariety of X′,
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