Global quantum geometric Langlands at irrational level
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
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∈\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.
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MANUSCRIPT 01
Global quantum geometric Langlands at irrational level
We prove the unramified quantum geometric Langlands equivalence for every connected simple complex algebraic group G and every level c∈\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{Bun}\nolimits _G(X)…
Full source abstract
We prove the unramified quantum geometric Langlands equivalence for every connected simple complex algebraic group G and every level c∈\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{Bun}\nolimits _G(X) and \mathop{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.
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