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

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.

References in corpus (2)

• Sheaves of categories and the notion of 1-affineness
• Shtukas for reductive groups and Langlands correspondence for function fields

Cited by in corpus (6)

• Coherent sheaves on the stack of Langlands parameters
• Geometric theta-lifting for the dual pair SO_{2m}, Sp_{2n}
• Duality for automorphic sheaves with nilpotent singular support
• Automorphic functions as the trace of Frobenius
• The Arinkin-Gaitsgory temperedness conjecture
• Whittaker coefficients of geometric Eisenstein series