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Archiv der Mathematik

, Volume 113, Issue 6, pp 593–601 | Cite as

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

  • Cornelius Greither
  • Sören KleineEmail author
Article
  • 60 Downloads

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.

Keywords

Leopoldt’s conjecture Pseudo-null module Unbounded lambda invariants 

Mathematics Subject Classification

11R23 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für theor. Informatik, Mathematik und ORUniversität der Bundeswehr MünchenNeubibergGermany

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