New York Journal of Mathematics
Volume 20 (2014) 759-778


Andrea Bandini, Francesc Bars, and Ignazio Longhi

Characteristic ideals and Iwasawa theory

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Published: August 26, 2014
Keywords: Characteristic ideals; Iwasawa theory; Krull rings; class groups
Subject: 11R23; 13F25

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)≅Zp.


F. Bars supported by MTM2013-40680-P
I. Longhi supported by National Science Council of Taiwan, grant NSC100-2811-M-002-079

Author information

Andrea Bandini:
Dipartimento di Matematica e Informatica, Università degli Studi di Parma, Parco Area delle Scienze, 53/A - 43124 Parma (PR), Italy

Francesc Bars:
Departament Matemàtiques, Edif. C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia

Ignazio Longhi:
Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, 111 Ren Ai Road, Dushu Lake Higher Education Town, Suzhou Industrial Park, Suzhou, Jiangsu, 215123, China