Abstract
From the assumption that Leopoldt’s conjecture fails and some mild extra assumptions, we deduce the existence of multiple \(\mathbb {Z}_p\)-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.
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Greither, C., Kleine, S. The structure of higher-dimensional Iwasawa modules under a far-fetched assumption. Arch. Math. 113, 593–601 (2019). https://doi.org/10.1007/s00013-019-01363-0
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DOI: https://doi.org/10.1007/s00013-019-01363-0