Non-abelian Hodge Theory, Hitchin Fibrations, and Geometric Langlands — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Non-abelian Hodge theory provides a triple equivalence (Dolbeault/de Rham/Betti) that underpins Geometric Langlands, with Hitchin's system as the integrable core, and Donagi's work extends this to direct images via harmonic bundles and twistor D-modules. | MATH: The central object is the **Hitchin fibration** h: ℳH → 𝒜, where ℳH is the moduli of stable Higgs bundles (E,ϕ) on a curve C, ϕ ∈ H0(C, End(E)⊗ KC). The **non-abelian Hodge correspondence** is the homeomorphism (not holomorphic) between: - **Dolbeault**: ℳDol = {(E,ϕ)}/equivalence - **de Rham**: ℳdR = {flat connections ∇} - **Betti**: ℳB = Hom(π1(C), G)/G (character variety) The **Hitchin system** is a completely integrable system: dim ℳH = 2d, with \(d = \dim \mathcal{A} = \frac{1}{2}\dim \mathcal{M}_H =
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026nonabelian,
title = {{Non-abelian Hodge Theory, Hitchin Fibrations, and Geometric Langlands — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23430932},
url = {https://zenodo.org/records/23430932},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-abelian Hodge Theory, Hitchin Fibrations, and Geometric Langlands — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/17
PB - Zenodo
DO - 10.5281/zenodo.23430932
UR - https://zenodo.org/records/23430932
AB - FINDING: Non-abelian Hodge theory provides a triple equivalence (Dolbeault/de Rham/Betti) that underpins Geometric Langlands, with Hitchin's system as the integrable core, and Donagi's work extends this to direct images via harmonic bundles and twistor D-modules. | MATH: The central object is the **Hitchin fibration** h: ℳ_H → 𝒜, where ℳ_H is the moduli of stable Higgs bundles (E,ϕ) on a curve C, ϕ ∈ H^0(C, End(E)⊗ K_C). The **non-abelian Hodge correspondence** is the homeomorphism (not holomorphic) between: - **Dolbeault**: ℳ_Dol = {(E,ϕ)}/equivalence - **de Rham**: ℳ_dR = {flat connections ∇} - **Betti**: ℳ_B = Hom(π_1(C), G)/G (character variety) The **Hitchin system** is a completely integrable system: dim ℳ_H = 2d, with \(d = \dim \mathcal{A} = \frac{1}{2}\dim \mathcal{M}_H = Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -