The Stacks project

Remark 42.33.5. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X \to Y$ and $Y' \to Y$ be morphisms of schemes locally of finite type over $S$. Let $X' = Y' \times _ Y X$. Then there is an obvious restriction map

\[ A^ p(X \to Y) \longrightarrow A^ p(X' \to Y'),\quad c \longmapsto res(c) \]

obtained by viewing a scheme $Y''$ locally of finite type over $Y'$ as a scheme locally of finite type over $Y$ and settting $res(c) \cap \alpha '' = c \cap \alpha ''$ for any $\alpha '' \in \mathop{\mathrm{CH}}\nolimits _ k(Y'')$. This restriction operation is compatible with compositions in an obvious manner.

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