On tamely ramified pro-<i>p</i>-extensions over -extensions of

Itoh, Tsuyoshi; Mizusawa, Yasushi

doi:10.1017/s0305004113000637

Cited by 6 publications

(7 citation statements)

References 19 publications

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“…Therefore G S (k) is not p-adic analytic. Since [16,31,33]). Then G S (Q) is p-adic analytic, and actually there exists such S of cardinality |S| = 2 + δ p,2 .…”

Section: Relation Rank and Thementioning

confidence: 97%

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On pro-𝑝 link groups of number fields

Mizusawa

2019

Trans. Amer. Math. Soc.

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As an analogue of a link group, we consider the Galois group of the maximal pro-p-extension of a number field with restricted ramification which is cyclotomically ramified at p, i.e., tamely ramified over the intermediate cyclotomic Z p -extension of the number field. In some basic cases, such a pro-p Galois group also has a Koch type presentation described by linking numbers and mod 2 Milnor numbers (Rédei symbols) of primes. Then the pro-2 Fox derivative yields a calculation of Iwasawa polynomials analogous to Alexander polynomials.

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“…Therefore G S (k) is not p-adic analytic. Since [16,31,33]). Then G S (Q) is p-adic analytic, and actually there exists such S of cardinality |S| = 2 + δ p,2 .…”

Section: Relation Rank and Thementioning

confidence: 97%

“…All sets S with prometacyclic G S (Q cyc ) have been characterized arithmetically (cf. [16,31,33]). Then G S (Q) is p-adic analytic, and actually there exists such S of cardinality |S| = 2 + δ p,2 .…”

Section: 3mentioning

confidence: 99%

On pro-𝑝 link groups of number fields

Mizusawa

2019

Trans. Amer. Math. Soc.

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“…Hence by Proposition 4.5, if p q−1 p ≡ 1 (mod q) then X S (K) Z/p d Z for every Z pextension K/k. (See also, e.g., [13] for the case of the cyclotomic Z p -extension of Q.) REMARK 4.7.…”

Section: Sufficient Conditionsmentioning

confidence: 97%

“…For this subsection, see also [21], [24], [18], [14], [13], etc. Let K be a Z p -extension of an imaginary quadratic field k, and K n the nth layer of K/k for n ≥ 0 (recall that K 0 = k).…”

Section: Multiplicative Groups Of Residue Classesmentioning

confidence: 99%

On Tamely Ramified Iwasawa Modules for $\Zp$-extensions of Imaginary Quadratic Fields

Itoh¹,

Takakura²

2014

Tokyo J. Math.

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“…Proof. We use the result given in [17] (see also [9]). Let S = {q 1 , q 2 } be a set of distinct prime numbers satisfying the condition of [17,Theorem 1].…”

Section: Remark 43mentioning

confidence: 99%

Tamely ramified Iwasawa modules having no non-trivial pseudo-null submodules

Itoh¹

2018

J. Théor. Nombres Bordeaux

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Tamely ramified Iwasawa modules having no non-trivial pseudo-null submodules Tome 30, n o 3 (2018), p. 859-872. © Société Arithmétique de Bordeaux, 2018, tous droits réservés. L'accès aux articles de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/), implique l'accord avec les conditions générales d'utilisation (http://jtnb.cedram. org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l'utilisation à fin strictement personnelle du copiste est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedram Article mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.cedram.org/ Journal de Théorie des Nombres de Bordeaux 30 (2018), 859-872 Tamely ramified Iwasawa modules having no non-trivial pseudo-null submodules par Tsuyoshi ITOH Résumé. Ce travail fait suite à l'article [4] de Satoshi Fujii et l'auteur. Soient k un corps de nombres, p un nombre premier, et k c /k la Z p-extension cyclotomique. Pour un ensemble fini S de nombres premiers qui ne contient pas p, le module d'Iwasawa (par rapport à la prop extension abélienne maximale non ramifiée en dehors de S) a été étudié dans plusieurs articles. Nous donnons des exemples non-triviaux où X S (k c) a un sous-module fini non-nul avec k totalement réel. Nous donnons également un exemple similaire dans le cas de la Z ⊕2 p-extension d'un corps quadratique imaginaire. De plus, nous discutons en appendice des analogues faibles de la conjecture de Greenberg pour X S (k c).

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On tamely ramified pro-p-extensions over -extensions of

Cited by 6 publications

References 19 publications

On pro-𝑝 link groups of number fields

On pro-𝑝 link groups of number fields

On Tamely Ramified Iwasawa Modules for $\Zp$-extensions of Imaginary Quadratic Fields

Tamely ramified Iwasawa modules having no non-trivial pseudo-null submodules

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