On the reduction of an Iwasawa module
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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.
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.
참고문헌 (4)
- S. Fujii, "On Greenberg’s generalized conjecture for CM-fields", J. Reine Angew. Math, 731, pp.259~278 (2017)
- T. Kataoka, "A consequence of Greenberg’s generalized conjecture on Iwasawa invariants of Zp-extensions", Journal of Number Theory, 172(3), pp.200~233 (2017)
- J.Minardi, "Iwasawa modules for Z d p -extensions of algebraic number fields", Ph.D, pp.1986
- H. Taya, "Iwasawa Iinvariants andclass numbers of quadratic fields for the prime 3", Proc. Amer. Math. Soc, 128(5), pp.1285~1292 (1999)