## 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.

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