Lemma 42.16.1. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X$ be locally of finite type over $S$. Assume $X$ is integral.

If $Z \subset X$ is an integral closed subscheme, then the following are equivalent:

$Z$ is a prime divisor,

$Z$ has codimension $1$ in $X$, and

$\dim _\delta (Z) = \dim _\delta (X) - 1$.

If $Z$ is an irreducible component of an effective Cartier divisor on $X$, then $\dim _\delta (Z) = \dim _\delta (X) - 1$.

## Comments (0)

There are also: