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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.
Author: | Martin LüdtkeGND |
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URN: | urn:nbn:de:hebis:30:3-574318 |
Place of publication: | Frankfurt am Main |
Referee: | Jakob StixGND, 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): | ![]() |