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

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

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

## Comments (0)