Genus two curves with quaternionic multiplication and modular jacobian
We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for whi...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| 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:2117/1958 |
| Acceso en línea: | https://hdl.handle.net/2117/1958 |
| Access Level: | acceso abierto |
| Palabra clave: | Quaternions Modular curves Abelian varieties Genus two curves Quaternionic multiplication Modular abelian surfaces Corbes modulars Varietats abelianes Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) Classificació AMS::14 Algebraic geometry::14H Curves |
| Sumario: | We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex multiplication. We include an example of $A_f$ with quaternionic multiplication for which we find numerically a curve $C$ whose Jacobian is $A_f$ up to numerical approximation, and we prove that it has quaternionic multiplication and is isogenous to $A_f$. |
|---|