On the hyperbolic uniformization of Shimura curves with an Atkin-Lehner quotient of genus 0
[eng] The main goal of this thesis is to contribute to the explicit hyperbolic uniformization of Shimura curves. We will restrict to the case of curves attached to Eichler orders in rational quaternion algebras whose maximal Atkin-Lehner quotient has genus 0, which despite multiple differences bears...
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| Format: | doctoral thesis |
| Status: | Published version |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/102688 |
| Online Access: | https://hdl.handle.net/2445/102688 http://hdl.handle.net/10803/396134 |
| Access Level: | Open access |
| Keyword: | Funcions automòrfiques Formes automòrfiques Corbes Varietats de Shimura Invariants Superfícies de Riemann Automorphic functions Automorphic forms Curves Shimura varieties Riemann surfaces |
| Summary: | [eng] The main goal of this thesis is to contribute to the explicit hyperbolic uniformization of Shimura curves. We will restrict to the case of curves attached to Eichler orders in rational quaternion algebras whose maximal Atkin-Lehner quotient has genus 0, which despite multiple differences bears some resemblance to the classical modular case. We will provide an approach to obtain an explicit uniformization of these curves and some of their covers, together with several applications. We will illustrate all the applications with plenty of examples. |
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