The p-adic section conjecture for localisations of curves
- The $p$-adic section conjecture predicts that for a smooth, proper, hyperbolic curve $X$ over a $p$-adic field $k$, every section of the map of étale fundamental groups $\pi_1(X) \to G_k$ is induced by a unique $k$-rational point of $X$. While this conjecture is still open, the birational variant in which $X$ is replaced by its generic point is known due to Koenigsmann. Generalising an alternative proof of Pop, we extend this result to certain localisations of $X$ at a set of closed points $S$, an intermediate version in between the full section conjecture and its birational variant. As one application, we prove the section conjecture for $X_S$ whenever $S$ is a countable set of closed points.
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Dissertation Lüdtke 2020
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| Author: | Martin LüdtkeGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-574318 |
| Place of publication: | Frankfurt am Main |
| Referee: | Jakob StixORCiDGND, Annette WernerGND |
| Document Type: | Doctoral Thesis |
| Language: | English |
| Date of Publication (online): | 2020/12/14 |
| Year of first Publication: | 2020 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Granting Institution: | Johann Wolfgang Goethe-Universität |
| Date of final exam: | 2020/12/14 |
| Release Date: | 2020/12/22 |
| Tag: | anabelian geometry; arithmetic geometry; mathematics; section conjecture |
| Page Number: | 143 |
| HeBIS-PPN: | 474102297 |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Deutsches Urheberrecht |
