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PreprintCC BY 4.0Zenodo

Geometric Langlands Conjecture Proved: Galois-Automorphic Duality via Sheaves — E8 Intelligence Research

  • Andrew Stewart Caldin1
  1. 1Independent Researcher, United Kingdom
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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: Gal(ℚ̅/ℚ) ↔ Automorphic forms; geometric version: LocSysG ↔ D−modules on BunG; key objects: BunG (moduli of principal G-bundles), LocSysG (local systems), categorical equivalence via derived categories Db(QCoh(LocSysG)) ≅ Db(D−mod(BunG)). | 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 BunG 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

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Cite

BibTeXRIS
BibTeX
@misc{caldin2026geometric,
  title = {{Geometric Langlands Conjecture Proved: Galois-Automorphic Duality via Sheaves — E8 Intelligence Research}},
  author = {Andrew Stewart Caldin},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23465400},
  url = {https://zenodo.org/records/23465400},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Geometric Langlands Conjecture Proved: Galois-Automorphic Duality via Sheaves — E8 Intelligence Research
AU  - Andrew Stewart Caldin
PY  - 2026
DA  - 2026/10/19
PB  - Zenodo
DO  - 10.5281/zenodo.23465400
UR  - https://zenodo.org/records/23465400
AB  - 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: Gal(ℚ̅/ℚ) ↔ Automorphic forms; geometric version: LocSys_G ↔ D−modules on Bun_G; key objects: Bun_G (moduli of principal G-bundles), LocSys_G (local systems), categorical equivalence via derived categories D^b(QCoh(LocSys_G)) ≅ D^b(D−mod(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 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
ER  -