Remark: Family 019. The p -adic section conjecture

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

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.