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On the modularity level of modular abelian varieties over number fields
Gonzalez Jimenez, Enrique; Guitart Morales, Xavier
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. TN - Teoria de Nombres
Electronic version of an article published as "Journal of number theory", vol. 130, no 7, p. 1560-1570. DOI no 10.1016/j.jnt.2010.03.003.
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 A f 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)f dim B L = N dim B, where fL is the conductor of L
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica
Geometry, Algebraic
Abelian varieties
Varietats abelianes
Geometria algebraica
Article - Draft

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