On the modularity level of modular abelian varieties over number fields
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Defense date2010-07
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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 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
Description
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. <http://www.uam.es/personal_pdi/ciencias/engonz/research/papers/levelBB.pdf>
CitationGonzalez, E.; Guitart, X. On the modularity level of modular abelian varieties over number fields. "Journal of number theory", Juliol 2010, vol. 130, núm. 7, p. 1560-1570.
ISSN0022-314X
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