2025/05/28 by Anatoly Galikhanov, Galikhanov, Anatoly
Mathematics · Physics and Astronomy · #11F70 #14G32 #18N50 #55U40 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #F.1.1 #F.4.1 #FOS: Mathematics #G.0 #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2505.22558
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a pro-étale geometric object D_∞ arising naturally from the tower of Artin-Schreier extensions in characteristic 2, equipped with a canonical endofunctor O whose fixed points correspond to automorphic representations of GL2(\mathbbA_\mathbbF2). The main theorem establishes that invariant predicates on D_∞ parametrize cuspidal automorphic representations, preserving L-functions. We provide complete proofs using ∞-categorical techniques, explicit computations for small cases, and establish connections to discrete conformal field theory. As applications, we resolve the Carlitz-Drinfeld uniformization conjecture for function fields and compute previously unknown motivic cohomology groups. Our approach differs fundamentally from coalgebraic models by working internally in topoi and connecting to arithmetic geometry.