Bad Reduction of Genus Three Curves with Complex Multiplication

  • Irene Bouw
  • Jenny Cooley
  • Kristin Lauter
  • Elisa Lorenzo García
  • Michelle Manes
  • Rachel Newton
  • Ekin Ozman
Part of the Association for Women in Mathematics Series book series (AWMS, volume 2)

Abstract

Let C be a smooth, absolutely irreducible genus 3 curve over a number field M. Suppose that the Jacobian of C has complex multiplication by a sextic CM-field K. Suppose further that K contains no imaginary quadratic subfield. We give a bound on the primes \(\mathfrak{p}\) of M such that the stable reduction of C at \(\mathfrak{p}\) contains three irreducible components of genus 1.

MSC 2010:

11G15 14K22 15B33 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Irene Bouw
    • 1
  • Jenny Cooley
    • 2
  • Kristin Lauter
    • 3
  • Elisa Lorenzo García
    • 4
  • Michelle Manes
    • 5
  • Rachel Newton
    • 6
  • Ekin Ozman
    • 7
    • 8
  1. 1.Institute of Pure MathematicsUniversity of UlmUlmGermany
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK
  3. 3.Microsoft ResearchRedmondUSA
  4. 4.Mathematisch InstituutUniversiteit LeidenLeidenThe Netherlands
  5. 5.Department of MathematicsUniversity of HawaiiHonoluluUSA
  6. 6.Max Planck Institute for MathematicsBonnGermany
  7. 7.Mathematics DepartmentUniversity of Texas at AustinAustinUSA
  8. 8.Department of MathematicsBogazici UniversityIstanbulTurkey

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