Alexander Perry disproves the period-index conjecture (Colliot-Thélène, 2001); a flawed ChatGPT example was the starting point
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). His AI disclosure says the starting point was a flawed ChatGPT example of the right general shape. Perry found the correct construction himself (a generic K3 surface with a symplectic group action), with ChatGPT helping on literature and lattice calculations.
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- Status: preprint, not peer-reviewed
Science result
- Field
- mathematics / algebraic geometry / Brauer groups
- Problem
- Period-index conjecture (open since 2001)
- Result
- Varieties of every dimension d ≥ 3 with a Brauer class of period 2 and index 2^d, contradicting the conjecture; a corrected conjecture is proposed.
- AI system
- ChatGPT
- Human role
- Human-led: a wrong AI example inspired the construction; the human found and proved the correct one, with AI help on literature search and lattice calculations
- Verification
- Preprint by an expert in the field; not peer-reviewed
- Status
- pending
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.
Changelog
- 2026-09-30: created
Related events
Sources (1)
id: 2026-08-04-period-index-conjecture-false · updated 2026-09-30 · open in the interactive timeline