The structure of higher-dimensional Iwasawa modules under a far-fetched assumption

摘要

From the assumption that Leopoldt's conjecture fails and some mild extra assumptions, we deduce the existence of multiple Zpdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$mathbb {Z}_p$$end{document}-extensions whose Iwasawa modules are "large" in a precise sense. We are not aware of any constructions of such extensions that avoid our preposterously strong hypothesis.