A non-Archimedean analogue of Teichmüller space and its tropicalization
- 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.
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| Author: | Martin UlirschORCiDGND |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-636359 |
| DOI: | https://doi.org/10.1007/s00029-021-00651-4 |
| ISSN: | 1420-9020 |
| Parent Title (English): | Selecta Mathematica |
| Publisher: | Birkhäuser |
| Place of publication: | Basel [u.a.] ; Berlin |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2021/05/29 |
| Date of first Publication: | 2021/05/29 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2022/07/12 |
| Volume: | 27 |
| Issue: | 3, art. 39 |
| Page Number: | 34 |
| First Page: | 1 |
| Last Page: | 34 |
| Note: | Finally, we acknowledge support from the LOEWE-Schwerpunkt “Uniformisierte Strukturen in Arithmetik und Geometrie”. Open Access funding enabled and organized by Projekt DEAL. |
| Note: | Weitere MSC-Klassifikation: 14T20. |
| HeBIS-PPN: | 502474319 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 14-XX ALGEBRAIC GEOMETRY / 14Gxx Arithmetic problems. Diophantine geometry [See also 11Dxx, 11Gxx] / 14G22 Rigid analytic geometry |
| 14-XX ALGEBRAIC GEOMETRY / 14Hxx Curves / 14H10 Families, moduli (algebraic) | |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
