## 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): | Deutsches Urheberrecht |