The Stacks project

62.2 Conventions and notation

Please consult the chapter on Chow Homology and Chern Classes for our conventions and notation regarding cycles on schemes locally of finite type over a fixed Noetherian base, see Chow Homology, Section 42.7 ff.

In particular, if $X$ is locally of finite type over a field $k$, then $Z_ r(X)$ denotes the group of cycles of dimension $r$, see Chow Homology, Example 42.7.2 and Section 42.8. Given an integral closed subscheme $Z \subset X$ with $\dim (Z) = r$ we have $[Z] \in Z_ r(X)$ and if $X$ is quasi-compact, then $Z_ r(X)$ is free abelian on these classes.