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Proof of the geometric Langlands conjecture

Dennis GaitsgorySam RaskinDima ArinkinDario BeraldoLin ChenJoakim FaergemanKevin LinNick Rozenblyum

This page delivers no verdict; it presents claims and evidence with their sources. No theory in science is absolute. Method

For everyone

The Langlands programme aims to build a deep "dictionary" between number theory, geometry and symmetry, and is often called a "grand unified theory" of mathematics. In 2024 nine mathematicians announced a proof of its geometric form in a series of five papers of nearly 1,000 pages.

For specialists

The conjecture (characteristic zero, de Rham form) asserts an equivalence between the category of D-modules on the moduli stack Bun_G of G-bundles on a smooth projective curve X and the category of ind-coherent sheaves (with nilpotent singular support) on LocSys_Ǧ, the stack of local systems for the Langlands dual group. The series first constructs the functor from the automorphic to the spectral side and then shows that it is an equivalence.

Claims

Evidence

Supporting

Mathematical proof

The proof was posted to arXiv as five papers. Review by experts may take years because of its length.[1][2]

Challenging

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Connections

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Mathematics

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Sources

  1. PreprintGaitsgory, D.; Raskin, S. et al. (2024). Proof of the geometric Langlands conjecture I: construction of the functorarXiv:2405.03599archive
  2. PreprintGaitsgory, D.; Raskin, S. et al. (2024). Proof of the geometric Langlands conjecture V: the multiplicity one theoremarXiv:2409.09856archive

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Cite this page

APA

Athena contributors. (2026). Proof of the geometric Langlands conjecture. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/langlands/

BibTeX
@misc{athena_langlands,
  title        = {Proof of the geometric Langlands conjecture},
  author       = {{Athena contributors}},
  year         = {2026},
  howpublished = {\url{https://latifkedi.github.io/athena/en/d/langlands/}},
  note         = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}

Added: September 27, 2026 · Last changed: September 27, 2026 · Page history

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