Proves the unramified de Rham quantum geometric Langlands equivalence for every connected simple complex algebraic group on every smooth projective connected complex curve, at every shifted level c\in\mathbb C\setminus\mathbb Q. It identifies the full derived categories of twisted D-modules for the group and its Langlands dual, retaining all global forms and connected components.
Manuscript
Global quantum geometric Langlands at irrational level
October 4, 2026 · source · cite as \cite{OAI:Global-quantum-geometric-Langlands-at-irrational-level-October-4-2026}
We prove the unramified quantum geometric Langlands equivalence for every connected simple complex algebraic group G and every level c\in\mathbb C\setminus\mathbb Q, including non-real levels. For every smooth projective connected complex curve X, it identifies the full twisted D-module categories on \mathop{\mathrm{Bun}}\nolimits _G(X) and \mathop{\mathrm{Bun}}\nolimits _{G^\vee}(X) at the dual shifted levels c and -1/(rc), where r is the lacing number. The equivalence uses the given global forms and includes all connected components.
Result 069 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md