Paper detail

Characteristic ideals and Iwasawa theory

Let $Ł$ be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains $Ł_d$ and let $M$ be a finitely generated $Ł$-module which is the inverse limit of $Ł_d$-modules $M_d\,$. Under certain hypotheses on the rings $Ł_d$ and on the modules $M_d\,$, we define a pro-characteristic ideal for $M$ in $Ł$, 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 non-noetherian Iwasawa algebra $\Z_p[[\Gal(\calf/F)]]$, where $F$ is a function field of characteristic $p$ and $\Gal(\calf/F)\simeq\Z_p^\infty$.