The Weil-Moore anima refines the Weil group into a space with higher homotopy groups to improve its cohomological behavior for number fields.
Coherent sheaves on the stack of Langlands parameters
4 Pith papers cite this work. Polarity classification is still indexing.
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Proves a generic categorical local Langlands correspondence for many quasi-split reductive p-adic groups via a fully faithful functor from generic Bernstein blocks to ind-coherent sheaves on L-parameter moduli stacks, generalizing the GL_n case.
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.
Anabelomorphic p-adic fields induce isomorphic Langlands parameter stacks, yielding a conjecture relating Fargues-Scholze to anabelomorphy that holds for split tori.
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Igusa Stacks and the Cohomology of Shimura Varieties
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.