manuscripta mathematica

, Volume 98, Issue 1, pp 37–54

On curves of genus 2 with Jacobian of GL2-type

  • G. Cardona
  • J. González
  • J. C. Lario
  • A. Rio

DOI: 10.1007/s002290050123

Cite this article as:
Cardona, G., González, J., Lario, J. et al. manuscripta math. (1999) 98: 37. doi:10.1007/s002290050123

Abstract:

Ribet [Ri] has generalized the conjecture of Shimura–Taniyama–Weil to abelian varieties defined over Q,giving rise to the study of abelian varieties of GL2-type. In this context, all curves over Q of genus one have Jacobian variety of GL2-type. Our aim in this paper is to begin with the analysis of which curves of genus 2 have Jacobian variety of GL2-type. To this end, we restrict our attention to curves with rational Rosenhain model and non-abelian automorphism group, and use the embedding of this group into the endomorphism algebra of its Jacobian variety to determine if it is of GL2-type.

Mathematics Subject Classification (1991):14H40, 11G10, 11F11

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • G. Cardona
    • 1
  • J. González
    • 1
  • J. C. Lario
    • 1
  • A. Rio
    • 1
  1. 1.Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Pau Gargallo, 5, E-08028 Barcelona, Spain.¶e-mail: cardona@grec.upc.esES