When the total mass ZO(N ) (β , x) of WO(N ) is ﬁnite, we say that the pair (β , x) is admissible and we can consider the probability measure PO(N ) = ZO(N ) (β , x)−1WO(N ) .
Scaling limits of random planar maps with large faces
Then Z = `O ZO is a ﬁnite partition, and ZO is a locally closed subvariety of Z .
Exotic symmetric space over a finite field, II
Now using Serre’s theorem (see for example (Hartshorne, 1977, Corollary II.5.18)) and that every quasi-coherent sheaf on X is the ﬁltered union of coherent subsheafs, we get that ⊕l∈ZO(k) is a generator for Qco(X ) of ﬁnite pro jective dimension ≤ n by the previous.
A Lazard-like theorem for quasi-coherent sheaves