The Stacks project

Remark 81.26.3. In Situation 81.2.1 let $f : X \to Y$ be a morphism of good algebraic spaces over $B$. Then there is a canonical $\mathbf{Z}$-algebra map $A^*(Y) \to A^*(X)$. Namely, given $c \in A^ p(Y)$ and $X' \to X$, then we can let $f^*c$ be defined by the map $c \cap - : \mathop{\mathrm{CH}}\nolimits _ k(X') \to \mathop{\mathrm{CH}}\nolimits _{k - p}(X')$ which is given by thinking of $X'$ as an algebraic space over $Y$.


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