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

Jangheon Oh

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.


Keywords


Iwasawa invariants, generalized Greenberg conjecture, bi-quadratic fields

Subject classification

11R23

Sponsor(s)



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References


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