Example 37.73.8. Let k be a field and let X = \mathbf{P}^ n_ k be n-dimensional projective space over k. Lemma 37.73.5 applies to this by Constructions, Lemma 27.13.3. Hence the affine stratification number of \mathbf{P}^ n_ k is at most n. On the other hand, we have nonzero cohomology in degree n for some quasi-coherent modules on \mathbf{P}^ n_ k, see Cohomology of Schemes, Lemma 30.8.1. Using Proposition 37.73.7 we conclude that the affine stratification number of \mathbf{P}^ n_ k is equal to n.
Comments (0)