Our exposition · Extremely preliminary draft
Lech’s conjecture in equal characteristic
Our exposition of the equal-characteristic argument. We believe the proofs are correct, but this draft is much rougher than we would ordinarily circulate. Our current understanding and confidence are closer to those of referees assessing a proof than of authors who have fully developed and internalized every aspect of it. The revised proofs in Section 3 were also obtained using ChatGPT Astra.
We welcome corrections, suggestions, and pointers to earlier work that may deserve credit.
Note: This document was originally posted on October 5, 2026, and has since then had only minor updates. On October 6, 2026, OpenAI announced another proof of Lech's Conjecture (in full generality, not just the equi-characteristic case). Here is a link to that proof: OpenAI's proof of Lech's Conjecture.