Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 069-01. Global quantum geometric Langlands at irrational level
Manuscript map · lines 3875–3884
OpenAI@2026-10-07#rem:oai-p-069-01
Authors: OpenAI. Family 069.
Title: Global quantum geometric Langlands at irrational level.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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