Singular Support and Nilpotent Cones in Spectral Geometric Langlands — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: The spectral side of geometric Langlands is being rigorously constructed via singular support of coherent sheaves on quasi-smooth derived schemes, with nilpotent cones stratifying the category; elliptic curve case yields explicit irreducible components and simple-object bijections. | MATH: Core object: IndCoh𝒩(LocSyscheckG) — coherent sheaves with singular support in the global nilpotent cone 𝒩 ⊂ T*LocSyscheckG. Quasi-smoothness: 𝒪X has finite Tor-amplitude; singular support SS(ℱ) ⊂ T*X is a conical Lagrangian. For elliptic curves E, the stack Coh(E) stratification yields irreducible components of the global nilpotent cone; bijection: simple objects of PerN(Coh(E)) ↔ irreducible components of 𝒩E. No explicit numeric constants appear — the invariants are categorical (Lagrangian
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026singular,
title = {{Singular Support and Nilpotent Cones in Spectral Geometric Langlands — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446581},
url = {https://zenodo.org/records/23446581},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Singular Support and Nilpotent Cones in Spectral Geometric Langlands — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446581
UR - https://zenodo.org/records/23446581
AB - FINDING: The spectral side of geometric Langlands is being rigorously constructed via singular support of coherent sheaves on quasi-smooth derived schemes, with nilpotent cones stratifying the category; elliptic curve case yields explicit irreducible components and simple-object bijections. | MATH: Core object: IndCoh_𝒩(LocSys_checkG) — coherent sheaves with singular support in the global nilpotent cone 𝒩 ⊂ T^*LocSys_checkG. Quasi-smoothness: 𝒪_X has finite Tor-amplitude; singular support SS(ℱ) ⊂ T^*X is a conical Lagrangian. For elliptic curves E, the stack Coh(E) stratification yields irreducible components of the global nilpotent cone; bijection: simple objects of Per_N(Coh(E)) ↔ irreducible components of 𝒩_E. No explicit numeric constants appear — the invariants are categorical (Lagrangian Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -