Remarks on strongly modular Jacobian surfaces

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

Journal de Théorie des Nombres de Bordeaux (2011)

  • Volume: 23, Issue: 1, page 171-182
  • ISSN: 1246-7405

Abstract

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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].

How to cite

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Guitart, Xavier, and Quer, Jordi. "Remarks on strongly modular Jacobian surfaces." Journal de Théorie des Nombres de Bordeaux 23.1 (2011): 171-182. <http://eudml.org/doc/219792>.

@article{Guitart2011,
abstract = {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].},
affiliation = {Dept. Matemàtica Aplicada II Universitat Politècnica de Catalunya Carrer Colom 11 08222 Terrassa; Dept. Matemàtica Aplicada II Universitat Politècnica de Catalunya Carrer Jordi Girona 1-3 08028 Barcelona},
author = {Guitart, Xavier, Quer, Jordi},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Abelian varieties; Jacobians; modular varieties},
language = {eng},
month = {3},
number = {1},
pages = {171-182},
publisher = {Société Arithmétique de Bordeaux},
title = {Remarks on strongly modular Jacobian surfaces},
url = {http://eudml.org/doc/219792},
volume = {23},
year = {2011},
}

TY - JOUR
AU - Guitart, Xavier
AU - Quer, Jordi
TI - Remarks on strongly modular Jacobian surfaces
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2011/3//
PB - Société Arithmétique de Bordeaux
VL - 23
IS - 1
SP - 171
EP - 182
AB - 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].
LA - eng
KW - Abelian varieties; Jacobians; modular varieties
UR - http://eudml.org/doc/219792
ER -

References

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  3. X. Guitart, J. Quer, Modular abelian varieties over number fields. Submitted. Preprint available at http://arxiv.org/abs/0905.2550v1 Zbl1294.11096
  4. J. J. Cannon, W. Bosma (Eds.), Handbook of Magma Functions, Edition 2.15-13 (2009). 
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  7. J. Quer, Fields of definition of building blocks. Math. Comp. 78 (2009), pp. 537–554. Zbl1204.11091MR2448720
  8. K. A. Ribet, Abelian varieties over and modular forms. Modular curves and abelian varieties, Progress in Math., vol. 224 (2002), pp. 241–261. Zbl1092.11029MR2058653
  9. K. A. Ribet, Twists of modular forms and endomorphisms of abelian varieties. Math. Ann. 253 (1980), no. 1, 43–62. Zbl0421.14008MR594532
  10. V. Rotger, The field of moduli of quaternionic multiplication on abelian varieties. Int. J. Math. Math. Sci. 2004, no. 49-52, 2795–2808. Zbl1133.11312MR2146495
  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. Zbl0493.14028MR670072

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