On the modularity level of modular abelian varieties over number fields
Entity
UAM. Departamento de MatemáticasPublisher
ElsevierDate
2010-07-01Citation
10.1016/j.jnt.2010.03.003
Journal of Number Theory 130.7 (2010): 1560-1570
ISSN
0022-314X (print); 1096-1658 (online)DOI
10.1016/j.jnt.2010.03.003Funded by
This work was supported in part by grants MTM 2009-07291 and CCG08-UAM/ESP-3906. This work was supported in part by grants 2009 SGR 1220 and MTM2009-13060-C02-01Project
Gobierno de España. MTM2009-07291; Gobierno de España. MTM2009-13060-C02-01Editor's Version
https://doi.org/10.1016/j.jnt.2010.03.003Subjects
Conductors; Modular Abelian Varieties; MatemáticasRights
© 2010 Elsevier Inc.Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
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
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Google Scholar:González-Jiménez, Enrique
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Guitart, Xavier
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