OpenAI · 019-01 · 2026-09-24 · Number theory
Étale covers with a prescribed exterior sheet
preprints/Etale-covers-with-a-prescribed-exterior-sheet-September-24-2026
Family 019. The -adic section conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves that rational points on every smooth proper geometrically connected curve of genus at least two over a finite extension of correspond bijectively to conjugacy classes of sections of its full arithmetic étale fundamental group. It also proves Grothendieck's section conjecture over for the modular curves and of genus at least two.
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.
Preprint source and Lean scope
The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.
No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.