UC San Diego
When
Where
Title: The Fargues-Scholze Correspondence at Generic Parameters
Abstract: Fargues and Scholze conjecture an equivalence between ℓ-adic sheaves on the moduli stack of 𝐺-bundles on the Fargues-Fontaine curve and ind-coherent sheaves on the stack of 𝐿-parameters. On each side there is a natural way to attach skyscraper sheaves to classical objects, namely irreducible smooth representations and 𝐿-parameters. One might then naively expect these sheaves to map to each other under the equivalence in a way that encodes classical local Langlands, but this turns out not to be the case. In this talk we will use the perverse-coherent sheaf theory of the nilpotent cone to compute the images of these sheaves in each direction of the correspondence after restricting to the locus of generic parameters. Time permitting, we will give applications to 𝑡-exactness properties of the equivalence and Hecke operators at generic parameters, as well as the construction of non-semisimplified refinements of generic Fargues-Scholze parameters.