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.
The local-to-global principle for triangulated categories via dimension functions.J
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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.