Characteristic ideals and Iwasawa theory

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.