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.
4 Matthew Emerton, Toby Gee, and Eugen Hellmann
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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.
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The Categorical Local Langlands Correspondence and Anabelomorphy
Anabelomorphic p-adic fields induce isomorphic Langlands parameter stacks, yielding a conjecture relating Fargues-Scholze to anabelomorphy that holds for split tori.