Remark 42.42.2. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X$ be locally of finite type over $S$ satisfying the equivalent conditions of Lemma 42.42.1. Let $X = \coprod X_ n$ be the decomposition into open and closed subschemes such that every irreducible component of $X_ n$ has $\delta$-dimension $n$. In this situation we sometimes set

$[X] = \sum \nolimits _ n [X_ n]_ n \in \mathop{\mathrm{CH}}\nolimits ^0(X)$

This class is a kind of “fundamental class” of $X$ in Chow theory.

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