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 $\mathbb Z_p[[T,T_2,\cdots,T_d]]$ is pseudo-null if $M/TM$ is pseudo-null over $\mathbb Z_p[[T_2,\cdots,T_d]]$. 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

[1] S.Fujii, On Greenberg’s generalized conjecture for CM-fields, J.Reine Angew. Math. 731 (2017), 259–278. Google Scholar

[2] Google Scholar

[3] T.Kataoka, A consequence of Greenberg’s generalized conjecture on Iwasawa invariants of Zp- extensions, Journal of Number Theory 172 (3) (2017), 200–233. Google Scholar

[4] J.Minardi, Iwasawa modules for Zdp-extensions of algebraic number fields, Ph.D dissertation, University of Washington, 1986. Google Scholar

[5] H.Taya, Iwasawa Iinvariants andclass numbers of quadratic fields for the prime 3 , Proc. Amer. Math. Soc. 128 (5) (1999), 1285–1292. Google Scholar