Greenberg's conjecture and Iwasawa module of real biquadratic fields I.
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| Title: | Greenberg's conjecture and Iwasawa module of real biquadratic fields I. |
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| Authors: | Chems-Eddin, Mohamed Mahmoud1 (AUTHOR) 2m.chemseddin@gmail.com |
| Source: | Journal of Number Theory. Apr2026, Vol. 281, p224-266. 43p. |
| Subjects: | Quadratic fields, Cyclotomic fields |
| Abstract: | The main aim of this paper is to investigate Greenberg's conjecture for real biquadratic fields. More precisely, we propose the following problem: What are real biquadratic number fields k such that rank (A (k ∞)) = rank (A (k 1)) ? where A (k ∞) is the 2-Iwasawa module of k and A (k 1) is the 2-class group of k 1 the first layer of the cyclotomic Z 2 -extension of k. Moreover, we give several families of real biquadratic fields k such that A (k ∞) is trivial or isomorphic to Z / 2 n Z or Z / 2 Z × Z / 2 n Z , where n is a given positive integer. The reader can also find some results concerning the 2-rank of the class group of certain real triquadratic fields. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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