On categorical local langlands program for GL_n

2023/09/28 by Kieu Hieu Nguyen, Nguyen, Kieu Hieu · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2309.16505

Abstract

We study various moduli spaces of local Shtukas in the setting of Fargues' program for GL_n. In certain cases, this gives us an explicit description of the spectral action which was recently introduced by Fargues and Scholze. This description sheds light to the categorical local Langlands program for GL_n and allows us to construct Hecke eigensheaves associated to certain ℓ-adic Weil representations of rank n and to prove some parts of Fargues' conjecture. Moreover, by using this description, we can prove new cases of the Harris-Viehmann conjecture for non-basic Rapoport-Zink spaces and compute some parts of the cohomology of the Igusa varieties associated to GL_n.

Cited by

• On the non-generic part of cohomology of compact unitary Shimura varieties of signature (1,n)

Related

• Averaging functors in Fargues' program for GL_n
• Categorical local Langlands and torsion classes of some Shimura varieties
• Geometrization of the local Langlands correspondence
• The local Langlands conjecture for GL(n) over a p-adic field, n < p
• A note on the cohomology of moduli spaces of local shtukas