∑math20

Number theory · Result 008

The Deligne–Drinfeld conjecture

1 paperLean

Proves that the rational Grothendieck–Teichmüller Lie algebra, with the Ihara bracket, is freely generated by one element in each odd weight 3, 5, 7, …, resolving the Deligne–Drinfeld conjecture.

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▶Introduction: the problem and why it mattersin preparation
▶The presented solutionin preparation

Papers 1

First page of The Deligne-Drinfeld conjecture

The Deligne-Drinfeld conjecture

OpenAI · September 23, 2026

We prove the Deligne–Drinfeld conjecture: the rational Grothendieck–Teichmüller Lie algebra is freely generated by one element in every odd weight at least three, with the corresponding isomorphism after weight completion.

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Cite
@misc{OAI:The-Deligne-Drinfeld-conjecture-September-23-2026,
  author = {{OpenAI}},
  title = {{The Deligne--Drinfeld conjecture}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Deligne-Drinfeld-conjecture-September-23-2026/paper.pdf}{OAI:The-Deligne-Drinfeld-conjecture-September-23-2026}},
  year = {2026}
}

What was formalized in Lean

The following describes the scope of the Lean formalization related to the following accompanying paper(s):

Scope

The Deligne–Drinfeld conjecture predicts that the rational Grothendieck–Teichmüller Lie algebra is freely generated by one element in each odd weight \(3,5,7,\ldots\). The formalization establishes this for the rational solution space of antisymmetry, the three-term equation, and the four-strand pentagon with the Ihara bracket. It also gives the corresponding continuous isomorphism after completion by weight.

The regularized-transport proposition and graph-complex consequences are not included.

Comparator links

ResultComparator statement
Deligne–Drinfeld main statementDeligneDrinfeld.lean

Scope note on GitHub →