On 2-adic Lie Iterated Extensions of Number Fields Arising from a Joukowski Map

Mizusawa, Yasushi; Yamamoto, Kiyotatsu

doi:10.3836/tjm/1502179321

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…Thus we obtain the statement for N 0 6 ¼ ;. Ã We need the following result, which is a part of [17,Theorem 2.1] or [13,Proposition 1].…”

Section: Number Theoretic Partmentioning

confidence: 99%

Iterated towers of number fields by a quadratic map defined over the Gaussian rationals

Mizusawa¹,

Yamamoto²

2020

Proc. Japan Acad. Ser. A Math. Sci.

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An iterated tower of number fields is constructed by adding preimages of a base point by iterations of a rational map. A certain basic quadratic rational map defined over the Gaussian number field yields such a tower of which any two steps are relative bicyclic biquadratic extensions. Regarding such towers as analogues of Z 2 -extensions, we examine the parity of 2ideal class numbers along the towers with some examples.

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“…Thus we obtain the statement for N 0 6 ¼ ;. Ã We need the following result, which is a part of [17,Theorem 2.1] or [13,Proposition 1].…”

Section: Number Theoretic Partmentioning

confidence: 99%

Iterated towers of number fields by a quadratic map defined over the Gaussian rationals

Mizusawa¹,

Yamamoto²

2020

Proc. Japan Acad. Ser. A Math. Sci.

Self Cite

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show abstract

“…Remark 4.5. In the situation of Theorem 4.4, the inertia field of the prime lying over [11,14] etc.).…”

Section: {2}mentioning

confidence: 99%

“…On the other hand, by arguments similar to the proof of Iwasawa's p-divisibility theorem ( [4], see also [13,Theorem 10.4]), Theorem 1.2 for k with cyclic A(k) is also obtained under more general ramification condition (see [14, Theorem 2.1 and Corollary 2.3], also [11,Proposition 1]). In this paper, combining the ideas of these results, we give a generalization of Theorem 1.2 in more general situation where the number fields are not necessarily finite extensions of Q.…”

Section: Introductionmentioning

confidence: 99%