The derived category of a commutative ring is generated by residue fields under a sufficient condition with an obstruction, and the local-to-global principle holds if and only if the spectrum satisfies a topological property.
Distributivity, affineness, and the structure sheaf
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We observe that for a quasi-compact and quasi-separated scheme the structure sheaf generates the perfect complexes if and only if the lattice of thick subcategories is distributive if and only if the affinization map is 0-affine. Examples are discussed, including an example of a quasi-projective scheme which is not quasi-affine but for which these equivalent conditions hold.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Constructs non-rigid tensor-triangulated categories whose thick tensor-ideals form non-distributive lattices.
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The importance of being isolated
The derived category of a commutative ring is generated by residue fields under a sufficient condition with an obstruction, and the local-to-global principle holds if and only if the spectrum satisfies a topological property.
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Non-distributive lattices of thick tensor-ideals via trivial extensions
Constructs non-rigid tensor-triangulated categories whose thick tensor-ideals form non-distributive lattices.