Fargues-Scholze vs. classical parameters, and applications

Abstract: For general reductive groups over a $p$-adic local field, Fargues and Scholze constructed a (semi-simplified) local Langlands with many good properties. On the other hand, classical local Langlands correspondences are known for classical groups via endoscopy theory and theta lifting. We review the construction of Fargues-Scholze and related geometric objects, and prove these two correspondences are compatible for all unramified special orthogonal and unitary groups. As an application, we prove torsion vanishing results for orthogonal Shimura varieties, generalizing results of Caraiani-Scholze, Koshikawa, Santos and Hamann-Lee, etc.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar