Characteristic ideals and Iwasawa theory

Andrea Bandini, Francesc Bars, Ignazio Longhi

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

Let Λ be a nonnoetherian Krull domain which is the inverse limit of noetherian Krull domains Λd and let M be a finitely generated Λ-module which is the inverse limit of Λd-modules Md. Under certain hypotheses on the rings Λd and on the modules Md, we define a pro-characteristic ideal for M in Λ, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a nonnoetherian Iwasawa algebra ℤp[[Gal(F / F)]], where F is a function field of characteristic p and Gal(F / F) ≃ ℤ∞p.
Original languageEnglish
Pages (from-to)759-778
JournalNew York Journal of Mathematics
Volume20
Publication statusPublished - 1 Jan 2014

Keywords

  • Characteristic ideals
  • Class groups
  • Iwasawa theory
  • Krull rings

Fingerprint Dive into the research topics of 'Characteristic ideals and Iwasawa theory'. Together they form a unique fingerprint.

Cite this