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ℚ-curves and Abelian Varieties of GL2-type from Dihedral Genus 2 Curves

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Modular Curves and Abelian Varieties

Part of the book series: Progress in Mathematics ((PM,volume 224))

Abstract

In this paper we review some of the results in [3] about curves of genus 2 with dihedral group of automorphisms and apply Ellenberg-Skinner’s criterion (cf. [4]) to determine that one can find infinitely many of them with modular Jacobian.

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References

  1. Matthew Baker, Enrique González, Josep González and Bjorn Poonen. Finiteness results for modular curves of genus at least 2. Preprint, November 2002.

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  2. Gabriel Cardona, Josep González, Joan-Carles Lario and Anna Rio. On curves of genus 2 with jacobian of GL2-type. Manuscripta Math., 98(1):37–54, 1999.

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  3. Gabriel Cardona and Jordi Quer. Curves of genus 2 with group of automorphisms isomorphic to Ds or D12. Submitted, February 2002.

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  4. Jordan S. Ellenberg and Chris Skinner. On the modularity of Q-curves. Duke Math. J.,109(1):97–122, 2001.

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  5. Josep González and Joan-Carles Lario. Rational and elliptic parametrizations of Q-curves. J. Number Theory, 72(1):13–31, 1998.

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  6. Jordi Quer. Q-curves and abelian varieties of GL2-type. Proc. London Math. Soc., 81(3):285–317, 2000.

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© 2004 Springer Basel AG

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Cardona, G. (2004). ℚ-curves and Abelian Varieties of GL2-type from Dihedral Genus 2 Curves. In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_3

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  • DOI: https://doi.org/10.1007/978-3-0348-7919-4_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9621-4

  • Online ISBN: 978-3-0348-7919-4

  • eBook Packages: Springer Book Archive

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