TY  - THES
A1  - Lüdtke, Martin
T1  - The p-adic section conjecture for localisations of curves
N2  - 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.
KW  - mathematics
KW  - arithmetic geometry
KW  - anabelian geometry
KW  - section conjecture
Y1  - 2020
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/57431
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-574318
CY  - Frankfurt am Main
ER  -