2026-04-17T23:26:21Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1933622025-12-05T09:55:26Zcom_2072_1057col_2072_478917col_2072_478920

On the modularity level of modular abelian varieties over number fields González-Jiménez, Enrique Guitart Morales, Xavier Teoria de nombres Varietats abelianes Geometria algebraica Varietats de Shimura Number theory Abelian varieties Algebraic geometry Shimura varieties Let $f$ be a weight two newform for $\Gamma_1(N)$ 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 $\operatorname{Res}_{L / Q}(B)$, 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 $\mathcal{N}_L(B)$. Under some hypothesis it is possible to give global formulas relating this conductor with $N$. For instance, if $N$ is squarefree we find that $\mathcal{N}_L(B)$ belongs to $\mathbb{Z}$ and $\mathcal{N}_L(B) \mathfrak{f}_L^{\operatorname{dim} B}=N^{\operatorname{dim} B}$, where $\mathfrak{f}_L$ is the conductor of $L$. 2023-02-09T14:24:31Z 2023-02-09T14:24:31Z 2010-07 2023-02-09T14:24:31Z info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion 0022-314X https://hdl.handle.net/2445/193362 650040 eng Versió postprint del document publicat a: https://doi.org/10.1016/j.jnt.2010.03.003 Journal of Number Theory, 2010, vol. 130, num. 7, p. 1560-1570 https://doi.org/10.1016/j.jnt.2010.03.003 (c) Elsevier, 2010 info:eu-repo/semantics/openAccess 11 p. application/pdf Elsevier Articles publicats en revistes (Matemàtiques i Informàtica)