Alexander Perry disproves the period-index conjecture
A flawed ChatGPT example was the starting point
Event confirmedAwaiting review
Importance: major (4 of 5)The takeaway
Alexander Perry posted counterexamples to the period-index conjecture for Brauer classes: d-dimensional varieties (d ≥ 3) with a Brauer class of period 2 and index 2^d (arXiv 2608.03684; v1 4 Aug, v2 3 Sep 2026).
Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- Major (4 of 5)
- Last verified
- 30 September 2026
Your AI and this story
- GPT-6 Astra96 days after its cutoff
- Claude Opus 5.535 days after its cutoff
- Gemini 4 Hydrogen126 days after its cutoff
- Grok 4.765 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 35 days before it.
Key facts
- Period-index conjecture: stated by Colliot-Thélène in 2001; predicts the index of a Brauer class on a d-dimensional variety divides period^(d−1)
- Result: failures in dimension 3 over Q and F_p(t), and in all dimensions d ≥ 3 over C and F_p((t)); the lower bound on the index uses a motivic obstruction, namely the non-existence of integral Hodge or Tate classes satisfying an equation mod 2
- Perry proposes a corrected period-index conjecture with corrections at small primes and proves its Hodge-theoretic counterpart
- AI disclosure, §1.7: prompted to use the paper’s Hodge-theoretic strategy, ChatGPT ‘produced a flawed example of a threefold X and Brauer class α’ that ‘had some features of our final solution’; ‘Drawing inspiration from this failed example, the author eventually discovered Theorem 1.3’; ChatGPT then ‘assisted with literature searches and lattice theory calculations’. The paper was written by the author
- Status: preprint, not peer-reviewed
What happened
Perry, who had earlier worked with de Jong on the Hodge theory of the period-index problem, asked ChatGPT to look for a counterexample along that strategy. The model’s example was wrong, but its shape pointed Perry to a correct construction built from K3 surfaces with symplectic group actions.
Why it matters
The period-index conjecture was a central open question on Brauer groups of function fields. It is also an example of an AI error being productive: the model gave the idea and a human supplied the correct mathematics.
What is disputed or not yet verified
| Verification | Preprint by an expert in the field; not peer-reviewed |
|---|
Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
Changes
- Filed