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

Characteristic ideals and Iwasawa theory / A. Bandini; F. Bars; I. Longhi. - In: NEW YORK JOURNAL OF MATHEMATICS. - ISSN 1076-9803. - 20:(2014), pp. 759-778.

### Characteristic ideals and Iwasawa theory

#### Abstract

Let $\L$ be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains $\L_d$ and let $M$ be a finitely generated $\L$-module which is the inverse limit of $\L_d$-modules $M_d\,$. Under certain hypotheses on the rings $\L_d$ and on the modules $M_d\,$, we define a pro-characteristic ideal for $M$ in $\L$, 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 $\Gal(\calf/F)\simeq\Z_p^\infty$.
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Characteristic ideals and Iwasawa theory / A. Bandini; F. Bars; I. Longhi. - In: NEW YORK JOURNAL OF MATHEMATICS. - ISSN 1076-9803. - 20:(2014), pp. 759-778.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2752700
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