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Bounds for Completely Decomposable Jacobians

  • Iwan Duursma
  • Jean-Yves Enjalbert

Abstract

A curve over the field of two elements with completely decomposable Jacobian is shown to have at most six rational points and genus at most 26. The bounds are sharp. The previous upper bound for the genus was 145. We also show that a curve over the field of q elements with more than q m /2 + 1 rational points has at least one Fobenius angle in the open interval (π/m, 3π/m). The proofs make use of the explicit formula method.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Iwan Duursma
    • 1
  • Jean-Yves Enjalbert
    • 2
  1. 1.University of Illinois at U-CUrbanaUSA
  2. 2.Université de LimogesLimoges CedexFrance

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