Cohen-Lenstra heuristics and the Spiegelungssatz; function fields

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Abstract

In this paper, we study the compatibility of Cohen-Lenstra heuristics with Leopoldt's Spiegelungssatz (= the reflection theorem) in the case of cyclic function fields. First, we prove a group-theoretical version of the Spiegelungssatz for cyclic function fields. Then we show the internal consistency of the function field analogue of Cohen-Lenstra heuristics in the case of cyclic function fields. It thus supports the validity of Cohen-Lenstra heuristics in function fields.

Original languageEnglish
Pages (from-to)187-199
Number of pages13
JournalJournal of Number Theory
Volume106
Issue number2
DOIs
StatePublished - Jun 2004

Keywords

  • Class groups
  • Cohen-Lenstra heuristics
  • Cyclic function field
  • Spiegelungssatz

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