Global quantum geometric Langlands at irrational level

What OpenAI claims

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 ∈ ℂ∖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.

Paper

1. Global quantum geometric Langlands at irrational level

   4 October 2026 · Preprint, not peer reviewed · PDF

   We prove the unramified quantum geometric Langlands equivalence for every connected simple complex algebraic group G and every level c ∈ ℂ∖ℚ, including non-real levels. For every smooth projective connected complex curve X, it identifies the full twisted D-module categories on Bun _G(X) and Bun _G^∨(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.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.