Remarks on strongly modular Jacobian surfaces
Journal de Théorie des Nombres de Bordeaux, Volume 23 (2011) no. 1, pp. 171-182.

In [3] we introduced the concept of strongly modular abelian variety. This note contains some remarks and examples of this kind of varieties, especially for the case of Jacobian surfaces, that complement the results of [3].

Dans [3] nous avons introduit la notion de variété abélienne fortement modulaire. Cette note contient quelques remarques et des exemples de ce type de variétés, surtout pour le cas des surfaces Jacobiennes, qui complètent les résultats de [3].

Published online:
DOI: 10.5802/jtnb.755
Xavier Guitart 1; Jordi Quer 2

1 Dept. Matemàtica Aplicada II Universitat Politècnica de Catalunya Carrer Colom 11 08222 Terrassa
2 Dept. Matemàtica Aplicada II Universitat Politècnica de Catalunya Carrer Jordi Girona 1-3 08028 Barcelona
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Xavier Guitart; Jordi Quer. Remarks on strongly modular Jacobian surfaces. Journal de Théorie des Nombres de Bordeaux, Volume 23 (2011) no. 1, pp. 171-182. doi : 10.5802/jtnb.755. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.755/

[1] S. Baba, H. Granath, Genus 2 curves with quaternionic multiplication. Canad. J. Math. 60 (2008), no. 4, 734–757. | MR: 2423455 | Zbl: 1163.11047

[2] J. González, J.-C. Lario, -curves and their Manin ideals. Amer. J. Math. 123 (2001), no. 3, 475–503. | MR: 1833149 | Zbl: 1035.14009

[3] X. Guitart, J. Quer, Modular abelian varieties over number fields. Submitted. Preprint available at http://arxiv.org/abs/0905.2550v1

[4] J. J. Cannon, W. Bosma (Eds.), Handbook of Magma Functions, Edition 2.15-13 (2009).

[5] E. E. Pyle, Abelian varieties over with large endomorphism algebras and their simple components over ¯. Modular curves and abelian varieties, Progress in Math., vol. 224 (2002), pp. 189–239. | MR: 2058652 | Zbl: 1116.11040

[6] J. Quer, Embedding problems over abelian groups and an application to elliptic curves. J. Algebra 237 (2001), no. 1, pp. 186–202. | MR: 1813898 | Zbl: 1040.12008

[7] J. Quer, Fields of definition of building blocks. Math. Comp. 78 (2009), pp. 537–554. | MR: 2448720 | Zbl: pre05813058

[8] K. A. Ribet, Abelian varieties over and modular forms. Modular curves and abelian varieties, Progress in Math., vol. 224 (2002), pp. 241–261. | MR: 2058653 | Zbl: 1092.11029

[9] K. A. Ribet, Twists of modular forms and endomorphisms of abelian varieties. Math. Ann. 253 (1980), no. 1, 43–62. | MR: 594532 | Zbl: 0421.14008

[10] V. Rotger, The field of moduli of quaternionic multiplication on abelian varieties. Int. J. Math. Math. Sci. 2004, no. 49-52, 2795–2808. | MR: 2146495 | Zbl: 1133.11312

[11] A. Weil, Adeles and algebraic groups. With appendices by M. Demazure and Takashi Ono. Progress in Mathematics, 23. Birkhuser, Boston, Mass., 1982. iii+126 pp. | MR: 670072 | Zbl: 0493.14028

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