The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support

2020/10/05 by D. Arinkin, Arinkin, D., Dennis Gaitsgory +9 · 5 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2010.01906

openalex publication_date 2020/10/05 · openalex created_date 2020/10/08 · openalex updated_date 2026/07/28

Abstract

We define a new geometric object--the stack of local systems with restricted variation. We formulate a version of the categorical geometric Langlands conjecture that makes sense for any constructible sheaf theory (such as l-adic sheaves). We formulate a conjecture that makes precise the connection between the category of automorphic sheaves and the space of automorphic functions.

Citations

• Constructible sheaves are holonomic
• Shtukas for reductive groups and Langlands correspondence for function\n fields
• Sheaves of categories and the notion of 1-affineness

Cited by

• Period sheaves via perverse pullbacks
• Potent categorical representations
• Local and global Langlands conjecture(s) over function fields
• Non-vanishing of quantum geometric Whittaker coefficients
• Rigid Algebras and Cospans

Related

• Singular support of coherent sheaves, and the geometric Langlands conjecture
• Geometric Langlands in positive characteristic from characteristic zero
• Between Coherent and Constructible Local Langlands Correspondences
• On the automorphic sheaves for GSp₄
• Geometric Realization of Whittaker Functions and the Langlands Conjecture