The derived category of a locally compact Hausdorff space X is smooth if and only if X is discrete and finite.
The sheaves-spectrum adjunction
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An ind-Banach framework defines overconvergent and holomorphic power series rings to endow C-algebras with analytic structures, yielding an abstract GAGA-type comparison.
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The derived category of a locally compact space is rarely smooth
The derived category of a locally compact Hausdorff space X is smooth if and only if X is discrete and finite.