The kernel of Ribet’s isogeny for genus three Shimura curves
There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the J...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2015 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/86355 |
| Acesso em linha: | https://hdl.handle.net/2117/86355 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Arithmetical algebraic geometry Shimura varieties Algebra Curves, Elliptic Àlgebra Corbes modulars Aritmètica Varietats de Shimura Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
| Resumo: | There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves. Moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of the new part of the Jacobian of the modular curve of level D such that the abelian variety quotient by c(D) is the jacobian of the curve XD. |
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