For qcqs schemes, the structure sheaf generates perfect complexes iff the thick subcategory lattice is distributive iff the affinization map is 0-affine.
Topology 39, 931-935 (2000)
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Distributivity, affineness, and the structure sheaf
For qcqs schemes, the structure sheaf generates perfect complexes iff the thick subcategory lattice is distributive iff the affinization map is 0-affine.