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
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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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math.AC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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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.