On rigid analytic uniformizations of Jacobians of Shimura curves
The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provide...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/334565 |
| Acceso en línea: | https://hdl.handle.net/2117/334565 |
| Access Level: | acceso abierto |
| Palabra clave: | Arithmetic Aritmètica Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Aritmètica |
| Sumario: | The main goal of this article is to give an explicit rigid analytic uniformization of the maximal toric quotient of the Jacobian of a Shimura curve over Q at a prime dividing exactly the level. This result can be viewed as complementary to the classical theorem of Cerednik and Drinfeld which provides rigid analytic uniformizations at primes dividing the discriminant. As a corollary, we offer a proof of a conjecture formulated by M. Greenberg in his paper on Stark-Heegner points and quaternionic Shimura curves, thus making Greenberg's construction of local points on elliptic curves over Q unconditional. |
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