## Abstract

Let Λ be a nonnoetherian Krull domain which is the inverse limit of noetherian Krull domains Λ_{d} and let M be a finitely generated Λ-module which is the inverse limit of Λ_{d}-modules M_{d}. Under certain hypotheses on the rings Λ_{d} and on the modules M_{d}, 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 ℤ_{p}[[Gal(F / F)]], where F is a function field of characteristic p and Gal(F / F) ≃ ℤ^{∞}_{p}.

Original language | English |
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Pages (from-to) | 759-778 |

Number of pages | 20 |

Journal | New York Journal of Mathematics |

Volume | 20 |

Publication status | Published - 2014 |

## Keywords

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