A consequence of Greenberg's generalized conjecture on Iwasawa invariants of Zp-extensions

被引：7

作者：

Kataoka, Takenori ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1138654, Japan

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 172卷

关键词：

Iwasawa theory; Greenberg's generalized conjecture; Iwasawa invariants; EXTENSIONS;

D O I：

10.1016/j.jnt.2016.08.008

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a prime number p and a number field k, let (k) over tilde be the compositum of all Z(p)-extensions of k. Greenberg's Generalized Conjecture (GGC) claims the pseudo-nullity of the unramified Iwasawa module X((k) over tilde) of (k) over tilde. It is known that, when k is an imaginary quadratic field, GGC has a consequence on the Iwasawa invariants associated to Z(P)-extensions of k. In this paper, we partially generalize it to arbitrary number fields k. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：200 / 233

页数：34

共 37 条

[21] ON VANDIVER CONJECTURE AND ZP-EXTENSIONS OF Q(ZETA-PN)
KERSTEN, I
MICHALICEK, J
[J]. JOURNAL OF NUMBER THEORY, 1989, 32 (03) : 371 - 386
[22] On capitulation of S-ideals in Zp-extensions
Sumida, H
[J]. JOURNAL OF NUMBER THEORY, 2001, 86 (01) : 163 - 174
[23] Iwasawa theory of elliptic curves at supersingular primes over Zp-extensions of number fields
Iovita, Adrian
Pollack, Robert
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2006, 598 : 71 - 103
[24] On an upper bound of λ-invariants of Zp-extensions over an imaginary quadratic field
Murakami, Kazuaki
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2019, 71 (03) : 1005 - 1026
[25] Invariants and coinvariants of class groups in Z(p) -extensions and Greenberg's Conjecture
Caldarola, Fabio
[J]. RIVISTA DI MATEMATICA DELLA UNIVERSITA DI PARMA, 2016, 7 (01): : 181 - 192
[26] On the Cyclicity of the Unramified Iwasawa Modules of the Maximal Multiple Zp-Extensions Over Imaginary Quadratic Fields
Miura, Takashi
Murakami, Kazuaki
Okano, Keiji
Otsuki, Rei
[J]. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2022, 34 (03): : 881 - 902
[27] On Greenberg?s generalized conjecture
Assim, J.
Boughadi, Z.
[J]. JOURNAL OF NUMBER THEORY, 2023, 242 : 576 - 602
[28] Greenberg's conjecture for Zpd-extensions
Bandini, A
[J]. ACTA ARITHMETICA, 2003, 108 (04) : 357 - 368
[29] Greenberg's conjecture and capitulation in Zdp-extensions
Bandini, Andrea
[J]. JOURNAL OF NUMBER THEORY, 2007, 122 (01) : 121 - 134
[30] ON THE STARK-SHINTANI CONJECTURE AND CYCLOTOMIC ZP-EXTENSIONS OF CLASS FIELDS OVER REAL QUADRATIC FIELDS
NAKAGAWA, J
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1984, 36 (04) : 577 - 588

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