Abstract
We give a simple proof of the fact that the localized Chern characters of Baum, Fulton and MacPherson commute with the refined Gysin homomorphisms of [3]. This has been proved in [3] in the context of bivariant intersection theory using the technique of deformation to the normal cone. Our proof is more elementary in the sense that it avoids such a deformation and relies on a commutativity formula of these Chern characters with effective Cartier divisors. From this formula we also derive easily that the localized Chern characters pass to rational equivalence.
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