On the modularity level of modular abelian varieties over number fields

Let f be a weight two newform for Γ1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety Af over certain number fields L. The strategy we follow is to compute the restriction of scalars ResL/Q(B), and then to apply Milne's...

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Detalles Bibliográficos
Autores: González-Jiménez, Enrique, Guitart, Xavier
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/711156
Acceso en línea:http://hdl.handle.net/10486/711156
https://dx.doi.org/10.1016/j.jnt.2010.03.003
Access Level:acceso abierto
Palabra clave:Conductors
Modular Abelian Varieties
Matemáticas
Descripción
Sumario:Let f be a weight two newform for Γ1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety Af over certain number fields L. The strategy we follow is to compute the restriction of scalars ResL/Q(B), and then to apply Milne's formula for the conductor of the restriction of scalars. In this way we obtain an expression for the local exponents of the conductor NL(B). Under some hypothesis it is possible to give global formulas relating this conductor with N. For instance, if N is squarefree, we find that NL(B) belongs to Z and NL(B)fLdimB=NdimB, where fL is the conductor of L