{"id":"openai-math/Etale-covers-with-a-prescribed-exterior-sheet","pdf":"https://github.com/openai/math/blob/main/preprints/Etale-covers-with-a-prescribed-exterior-sheet-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Etale-covers-with-a-prescribed-exterior-sheet-September-24-2026","tags":["algebraic-geometry","etale-covers","p-adic-geometry"],"score":0,"title":"Étale covers with a prescribed exterior sheet","domain":"Number theory","family":"019","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"Let X be a smooth proper hyperbolic curve over an algebraic closure of a p -adic local field. Given finitely many disjoint small open disks, we construct one connected finite étale cover with a sheet isomorphic to their entire exterior and with degree divisible by p on every connected component above each disk.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://www.minhyongkim.net/home/p-adic-section-conjecture","kind":"web","site":"minhyongkim.net","text":"Organisers: Magnus Carlson (Gävle), Minhyong Kim (Maxwell Institute Edinburgh and Kings College Cambridge), Padmavathi Srinivasan (Boston), Jakob Stix (Frankfurt) We will get together with the goal of understanding OpenAI's claimed proof of Grothendieck's section conjecture on fundamental groups","added":"2026-11-03","title":"Arithmetic, Geometry, Space, Time - P-adic Section Conjecture","author":"Minhyong Kim"}],"formalized":false,"family_title":"The local p -adic section conjecture and global consequences"}