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I am reading the paper "Relative Cycles and Chow Sheaves" due to Suslin and Voevodsky. Here we have the following definition:

Definition 2.1.2.

A morphism of schemes $p:X\rightarrow S$ is called an equidimensional morphism of dimension $r$ if the following conditions hold:

1.$p$ is a morphism of finite type.

2.The function $\dim(X/S)$ is constant and equals $r$.

3.Any irreducible component of $X$ dominates an irreducible component of $S$.

I would like to understand what the condition 3. means ... Thank you a lot!!!

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    $\begingroup$ It means that given any irreducible component $X_i$ of $X$, there is an irreducible component $S_j$ of $S$ such that $p(X_i)$ contains an open subset of $S_j$. Please use MSE for this type of questions. $\endgroup$
    – abx
    Commented Feb 26, 2021 at 14:29
  • $\begingroup$ Thank you abx!!... Why should I use MSE? $\endgroup$
    – Roxana
    Commented Feb 27, 2021 at 12:42
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    $\begingroup$ The question is fine, and indicates a participation in mathematics at a professional level. $\endgroup$
    – Todd Trimble
    Commented Mar 5, 2021 at 22:24

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