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
Willard,General topology, Dover Publications, Inc., Mineola, NY, 2004, Reprint of the 1970 original [Addison-Wesley, Reading, MA; MR0264581]
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Constructs functorial Igusa stacks for Hodge-type Shimura varieties, yielding a sheaf on Bun_G that controls cohomology and proves compatibility with the semisimple local Langlands correspondence of Fargues-Scholze while establishing torsion vanishing for proper cases.
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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