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The p-adic section conjecture

OpenAI · September 24, 2026

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This is an earlier edition (September 24, 2026). Current edition: The p-adic section conjecture, October 6, 2026.

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Cite

@misc{OAI:The-p-adic-section-conjecture-September-24-2026,
  author = {{OpenAI}},
  title = {{The p-adic section conjecture}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-p-adic-section-conjecture-September-24-2026/main.pdf}{OAI:The-p-adic-section-conjecture-September-24-2026}},
  year = {2026}
}

Family 019: The local p-adic section conjecture and global consequences

Proves that rational points on every smooth proper geometrically connected curve of genus at least two over a finite extension of ℚp correspond bijectively to conjugacy classes of sections of its full arithmetic étale fundamental group. It also proves Grothendieck's section conjecture over ℚ for the modular curves $X_0(N)$ and $X_1(N)$ of genus at least two.

Other papers in this family: