تقرير
Chabauty--Kim and the Section Conjecture for locally geometric sections
| العنوان: | Chabauty--Kim and the Section Conjecture for locally geometric sections |
|---|---|
| المؤلفون: | Betts, L. Alexander, Kumpitsch, Theresa, Lüdtke, Martin |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, Primary: 14H30. Secondary: 11G30, 14H25 |
| الوصف: | Let $X$ be a smooth projective curve of genus $\geq2$ over a number field. A natural variant of Grothendieck's Section Conjecture postulates that every section of the fundamental exact sequence for $X$ which everywhere locally comes from a point of $X$ in fact globally comes from a point of $X$. We show that $X/\mathbb{Q}$ satisfies this version of the Section Conjecture if it satisfies Kim's Conjecture for almost all choices of auxiliary prime $p$, and give the appropriate generalisation to $S$-integral points on hyperbolic curves. This gives a new "computational" strategy for proving instances of this variant of the Section Conjecture, which we carry out for the thrice-punctured line over $\mathbb{Z}[1/2]$. Comment: 53 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.09462 |
| رقم الأكسشن: | edsarx.2305.09462 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |