Reflection theorem for divisor class groups of relative quadratic function fields

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Abstract

We present the reflection theorem for divisor class groups of relative quadratic function fields. Let K be a global function field with constant field Fq. Let L1 be a quadratic geometric extension of K and let L2 be its twist by the quadratic constant field extension of K. We show that for every odd integer m that divides q + 1 the divisor class groups of L1 and L2 have the same m-rank.

Original languageEnglish
Pages (from-to)2127-2137
Number of pages11
JournalJournal of Number Theory
Volume128
Issue number7
DOIs
StatePublished - Jul 2008

Keywords

  • Divisor class group
  • Ideal class group
  • Quadratic function field
  • Rank of divisor class group
  • Reflection theorem

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