Korean J. Math. Vol. 29 No. 2 (2021) pp.267-269
DOI: https://doi.org/10.11568/kjm.2021.29.2.267

On the reduction of an Iwasawa module

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Published: May 10, 2021
Keywords:
Iwasawa invariants, generalized Greenberg conjecture, bi-quadratic fields
Mathematics Subject Classification:
11R23

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Jangheon Oh
Faculty of Mathematics and Statistics, Sejong University, Seoul 143-747, Korea.

Abstract

A finitely generated torsion module M for Zp[[T,T2,⋯,Td]] is pseudo-null if M/TM is pseudo-null over Zp[[T2,⋯,Td]]. This result is used as a tool to prove the generalized Greenberg's conjecture in certain cases. The converse may not be true. In this paper, we give examples of pseudo-null Iwasawa modules whose reduction are not pseudo-null.



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References

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