Geometric Langlands: Categorical Formulation via Moduli Stacks and Hecke Eigensheaves — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Geometric Langlands correspondence is being actively constructed via moduli stacks of local systems and Hecke eigensheaves, with recent advances by Gaitsgory, Raskin, and others toward a full categorical formulation. | MATH: The correspondence conjecturally identifies the derived category of coherent sheaves on the moduli stack of local systems LocSysG(Σ) with the derived category of D-modules on the moduli stack of principal G-bundles BunG(Σ), for a smooth projective curve Σ. Key objects: Hecke eigensheaves — D-modules ℱ on BunG satisfying Hμ(ℱ) ≅ ℱ boxtimes σμ(ℰ) for each Hecke correspondence, where σμ is the representation of the Langlands dual group L G with highest weight μ. The local version (Braverman) involves affine Grassmannian GrG = G(ℂ((t)))/G(ℂ[[t]]) and its c
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026geometric,
title = {{Geometric Langlands: Categorical Formulation via Moduli Stacks and Hecke Eigensheaves — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23553976},
url = {https://zenodo.org/records/23553976},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Geometric Langlands: Categorical Formulation via Moduli Stacks and Hecke Eigensheaves — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/22
PB - Zenodo
DO - 10.5281/zenodo.23553976
UR - https://zenodo.org/records/23553976
AB - FINDING: Geometric Langlands correspondence is being actively constructed via moduli stacks of local systems and Hecke eigensheaves, with recent advances by Gaitsgory, Raskin, and others toward a full categorical formulation. | MATH: The correspondence conjecturally identifies the derived category of coherent sheaves on the moduli stack of local systems LocSys_G(Σ) with the derived category of D-modules on the moduli stack of principal G-bundles Bun_G(Σ), for a smooth projective curve Σ. Key objects: Hecke eigensheaves — D-modules ℱ on Bun_G satisfying H_μ(ℱ) ≅ ℱ boxtimes σ_μ(ℰ) for each Hecke correspondence, where σ_μ is the representation of the Langlands dual group ^L G with highest weight μ. The local version (Braverman) involves affine Grassmannian Gr_G = G(ℂ((t)))/G(ℂ[[t]]) and its c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -