2023/10/06 by David J. Hansen, Hansen, David
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Automorphic form #Categorical variable #Conjecture #Duality (order theory) #FOS: Mathematics #Langlands dual group #Langlands program #Matching (statistics) #Mathematics #Number Theory (math.NT) #Pure mathematics #Representation Theory (math.RT) #Series (stratigraphy) #Statistics
paper · pdf · doi:10.48550/arxiv.2310.04533
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2023/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We formulate some refinements and complements to the categorical local Langlands conjecture of Fargues-Scholze. In particular, we state the expected compatibilities with Eisenstein series and duality, and explain some of their consequences. We also begin the process of matching t-structures on both sides. Notably, we introduce the so-called hadal t-structure on the automorphic side, which has good finiteness properties, and which conjecturally matches with a suitable perverse coherent t-structure on the spectral side.