Lemma 62.5.10. Let g : S' \to S be a bijective morphism of schemes which induces isomorphisms of residue fields. Let f : X \to S be locally of finite type. Set X' = S' \times _ S X. Let r \geq 0. Then base change by g determines a bijection between the group of families of r-cycles on fibres of X/S and the group of families of r-cycles on fibres of X'/S'.
Proof. Omitted. \square
Comments (0)