The global quantum geometric Langlands conjecture at irrational level

Theorem 1.1: for every connected simple complex algebraic group $G$ , every smooth projective connected complex curve $X$ and every $c\in\mathbb C\setminus\mathbb Q$ (including non-real $c$ ) there is an equivalence $D_c(\mathrm{Bun}_G(X))\simeq D_{-1/(rc)}(\mathrm{Bun}_{G^\vee}(X))$ of presentable DG categories, characterized by its localization-Whittaker comparison and intertwining central torsor actions with transgression local systems. It does not treat rational levels, ramification, the Betti setting, or non-simple reductive groups.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Oct 4, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The global quantum geometric Langlands conjecture at irrational level · Quantum geometric Langlands, irrational level

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

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VibeMathed record: The global quantum geometric Langlands conjecture at irrational level

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against the conjecture in the cited normalization; it gives the unramified de Rham equivalence for every connected simple $G$ , every smooth projective connected curve and every $c\in\mathbb C\setminus\mathbb Q$ , with given global forms and all connected components, characterized by a localization-Whittaker comparison. Scope limits stated by the paper: irrational levels only (rational levels, including the critical and integral ones, are excluded), unramified only, de Rham setting. The argument depends on the proof of ordinary geometric Langlands (Gaitsgory, Raskin and coauthors) and on other large published inputs. No Lean formalization exists for this family. The proof was not refereed.

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The global quantum geometric Langlands conjecture at irrational level

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Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Stoyanovsky, Quantum Langlands duality and conformal field theory (2006)

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Stoyanovsky, Quantum Langlands duality and conformal field theory (2006) evidence for this event

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