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.
|Journal||New York Journal of Mathematics|
|Publication status||Published - 1 Jan 2014|
- Characteristic ideals
- Class groups
- Iwasawa theory
- Krull rings