Categorical p-adic Langlands: Galois–GL₂ correspondence via depth-zero supercuspidals — E8 Intelligence Research

FINDING: The categorical p-adic Langlands program (arXiv 2210.01404) formalizes a functorial correspondence between p-adic Galois representations and p-adic Banach/analytic representations of GL₂, with explicit mod-ℓ depth-zero supercuspidal cases (Chenji Fu) providing concrete test instances. MATH: - Core object: A category equivalence (or derived functor) between \( Repcont(G_F) \) (p-adic Galois side) and \( Repcont(GL_2(F)) \) (p-adic representation side), where \(F\) is a p-adic field. - Key structures: Banach space representations, locally analytic representations, and the "categorical" refinement via derived categories or \(∞\)-categories. - Explicit case (Fu): mod-\(\) categorical local Langlands for depth-zero supercuspidal representations of \(GL_2(F)\) — involves Weil group inertia invariants, tame characters, and explicit functors between categories of \(F̄_\)-repres Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com