Definition 76.3.1. In Situation 76.2.1.

We say $\mathcal{F}$ is

*pure above $y$*if**none**of the equivalent conditions of Lemma 76.2.5 hold.We say $\mathcal{F}$ is

*universally pure above $y$*if there does not exist any impurity of $\mathcal{F}$ above $y$.We say that $X$ is

*pure above $y$*if $\mathcal{O}_ X$ is pure above $y$.We say $\mathcal{F}$ is

*universally $Y$-pure*, or*universally pure relative to $Y$*if $\mathcal{F}$ is universally pure above $y$ for every $y \in |Y|$.We say $\mathcal{F}$ is

*$Y$-pure*, or*pure relative to $Y$*if $\mathcal{F}$ is pure above $y$ for every $y \in |Y|$.We say that $X$ is

*$Y$-pure*or*pure relative to $Y$*if $\mathcal{O}_ X$ is pure relative to $Y$.

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