Everywhere Ramified Towers of Global Function Fields

  • Iwan Duursma
  • Bjorn Poonen
  • Michael Zieve
Conference paper

DOI: 10.1007/978-3-540-24633-6_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2948)
Cite this paper as:
Duursma I., Poonen B., Zieve M. (2004) Everywhere Ramified Towers of Global Function Fields. In: Mullen G.L., Poli A., Stichtenoth H. (eds) Finite Fields and Applications. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg

Abstract

We construct a tower of function fields F0 ⊂ F1 ⊂ ... over a finite field such that every place of every Fi ramifies in the tower and lim genus(Fi)/[Fi : F0] < ∞. We also construct a tower in which every place ramifies and limNFi/[Fi : F0] > 0, where NFi is the number of degree-1 places of Fi. These towers answer questions posed by Stichtenoth at Fq7.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Iwan Duursma
    • 1
  • Bjorn Poonen
    • 2
  • Michael Zieve
    • 3
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  3. 3.Center for Communications ResearchPrincetonUSA

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