Definition 37.70.4. Let $X$ be a nonempty quasi-compact and quasi-separated scheme. The affine stratification number is the smallest integer $n \geq 0$ such that the following equivalent conditions are satisfied

1. there exists a finite affine stratification $X = \coprod _{i \in I} X_ i$ where $I$ has length $n$,

2. there exists an affine stratification $X = X_0 \amalg X_1 \amalg \ldots \amalg X_ n$ with index set $\{ 0, \ldots , n\}$.

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