Using six functor formalisms, the authors prove that hypercomplete locally compact ANR homology manifolds are cohomologically smooth, that compact ANR homology manifolds are Poincaré duality complexes with Spivak tangent fibration as dualizing sheaf, introduce homotopy manifolds, and show that homot
The sheaves-spectrum adjunction
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The derived category of a locally compact Hausdorff space X is smooth if and only if X is discrete and finite.
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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Homology manifolds via six functor formalisms
Using six functor formalisms, the authors prove that hypercomplete locally compact ANR homology manifolds are cohomologically smooth, that compact ANR homology manifolds are Poincaré duality complexes with Spivak tangent fibration as dualizing sheaf, introduce homotopy manifolds, and show that homot
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Analytification for Complex Geometry Revisited
An ind-Banach framework defines overconvergent and holomorphic power series rings to endow C-algebras with analytic structures, yielding an abstract GAGA-type comparison.