TY  - JOUR
A1  - Ulirsch, Martin
T1  - A non-Archimedean analogue of Teichmüller space and its tropicalization
T2  - Selecta Mathematica
N2  - In this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue of Teichmüller space T¯g whose points are pairs consisting of a stable projective curve over a non-Archimedean field and a Teichmüller marking of the topological fundamental group of its Berkovich analytification. This construction is closely related to and inspired by the classical construction of a non-Archimedean Schottky space for Mumford curves by Gerritzen and Herrlich. We argue that the skeleton of non-Archimedean Teichmüller space is precisely the tropical Teichmüller space introduced by Chan–Melo–Viviani as a simplicial completion of Culler–Vogtmann Outer space. As a consequence, Outer space turns out to be a strong deformation retract of the locus of smooth Mumford curves in T¯g.
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63635
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-636359
SN  - 1420-9020
N1  - Finally, we acknowledge support from the LOEWE-Schwerpunkt “Uniformisierte Strukturen in Arithmetik und Geometrie”. Open Access funding enabled and organized by Projekt DEAL.
N1  - Weitere MSC-Klassifikation: 14T20.
VL  - 27
IS  - 3, art. 39
SP  - 1
EP  - 34
PB  - Birkhäuser
CY  - Basel [u.a.] ; Berlin
ER  -