TL;DR
This paper constructs the finite Langlands correspondence for connected reductive groups over finite fields and explores its relation to the categorical local Langlands correspondence.
Contribution
It introduces the finite Langlands correspondence and analyzes its connection with the categorical local Langlands correspondence.
Findings
Establishment of the finite Langlands correspondence for reductive groups over finite fields
Analysis of the relationship between finite and categorical local Langlands correspondences
Foundational framework for future research in finite field Langlands theory
Abstract
We construct the Langlands correspondence for connected reductive groups over finite fields, which we call the finite Langlands correspondence. We discuss also its relation with the categorical local Langlands correspondence.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory