Definition 37.73.4. 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\} .
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