Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 019-02. The p-adic section conjecture
Manuscript map · lines 2885–2894
OpenAI@2026-10-07#rem:oai-p-019-02
Authors: OpenAI. Family 019.
Title: The p-adic section conjecture.
Abstract: We prove the local p-adic section conjecture for smooth proper geometrically connected curves of genus at least two, over every finite extension of ℚp. Combined with established finite-descent theorems, this also yields the global section conjecture for smooth proper geometrically connected curves of genus at least two over number fields when their finite-cover descent locus equals their rational points; this includes $X_0(N)$ and $X_1(N)$ of genus at least two over ℚ.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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