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