This problem has Hartshorne Height 2 and volume 2; I.1.7 can be used to solve it.
Using I.1.7 you have that is quasi compact. So any cover can be taken to be finite. No elements of the direct limit sheaf are equivalence classes of elements: if there is k bigger than i,j such that the images of a,b agree in . In words, they agree if they agree far enough down the system.
- Show that finite covers allow the sheaf axioms to be checked by checking them on a sheaf of the system that is sufficiently far down in the system.
- If is already a sheaf then