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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Author:Martin LüdtkeGND
Place of publication:Frankfurt am Main
Referee:Jakob StixGND, Annette WernerGND
Document Type:Doctoral Thesis
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
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht