{"id":"doi:10.5281/zenodo.23465399","kind":"article","title":"Geometric Langlands Conjecture Proved: Galois-Automorphic Duality via Sheaves — E8 Intelligence Research","authors":["Andrew Stewart Caldin"],"author_count":1,"year":2026,"published":"2026-10-19","venue":"Zenodo (CERN European Organization for Nuclear Research)","cited_by":0,"doi":"10.5281/zenodo.23465399","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.5281/zenodo.23465399","archive_url":"https://space-kitty.com/papers/doi:10.5281/zenodo.23465399","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W7222972515","pdf_url":null,"abstract":"FINDING: Recent proof of the geometric Langlands conjecture (2024, by Gaitsgory et al.) completes a central pillar of the Langlands program, linking Galois representations to automorphic forms via sheaves on moduli stacks. | MATH: Core duality: \\( \\text{Gal}(\\bar{\\mathbb{Q}}/\\mathbb{Q}) \\leftrightarrow \\text{Automorphic forms} \\); geometric version: \\( \\text{LocSys}_G \\leftrightarrow \\text{D-modules on Bun}_G \\); key objects: \\( \\text{Bun}_G \\) (moduli of principal \\(G\\)-bundles), \\( \\text{LocSys}_G \\) (local systems), categorical equivalence via derived categories \\( D^b(\\text{QCoh}(\\text{LocSys}_G)) \\cong D^b(\\text{D-mod}(\\text{Bun}_G)) \\). | CONNECTION: The geometric Langlands correspondence is built on **root systems** (Dynkin diagrams) and **affine Kac-Moody algebras** — crystallographic symmetry groups (Weyl groups) are intrinsic. The moduli spaces \\( \\text{Bun}_G \\) carry **Hecke eigensheaves** whose eigenvalues are local systems — this mirrors the **harmonic ratio structure** o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Advanced Algebra and Geometry"],"details":null,"provenance":"openalex","attribution":"Abstract of \"Geometric Langlands Conjecture Proved: Galois-Automorphic Duality via Sheaves — E8 Intelligence Research\" by Andrew Stewart Caldin, https://doi.org/10.5281/zenodo.23465399, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.","topics":[{"slug":"landmark-math-results","name":"Landmark Results in Pure Mathematics","domain_slug":"math-cs"}],"cited_in_dossiers":[]}