ℓ-class groups of fields in Kummer towers
Li, Jianing (Shandong University. Research Center for Mathematics and Interdisciplinary Sciences.)
Ouyang, Yi (University of Science and Technology of China. CAS Wu Wen-Tsun Key Laboratory of Mathematics.)
Xu, Yue (University of Science and Technology of China. CAS Wu Wen-Tsun Key Laboratory of Mathematics.)
Zhang, Shenxing (University of Technology, Hefei, China. School of Mathematics)

Data:	2022
Resum:	Let ℓ and b be prime numbers and Kn,m = Q(p1 n , ζ2'm). We study the '-class group of Kn,m in this paper. When ' = 2, we determine the structure of the 2-class group of Kn,m for all (n, m) ∈ Z 2 ≥0 in the case p ≡ 3, 5 mod 8, and for (n, m) = (n, 0), (n, 1), or (1, m) in the case p ≡ 7 mod 16, generalizing the results of Parry about the 2-divisibility of the class number of K2,0. We also obtain results about the '-class group of Kn,m when ' is odd and in particular when ' = 3. The main tools we use are class field theory, including Chevalley's ambiguous class number formula and its generalization by Gras, and a stationary result about the '-class groups in the 2-dimensional Kummer tower {Kn,m}.
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Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Kummer tower ; Class group ; Ambiguous class number formula
Publicat a:	Publicacions matemàtiques, Vol. 66 Núm. 1 (2022) , p. 235-267 (Articles) , ISSN 2014-4350

Adreça original: https://raco.cat/index.php/PublicacionsMatematiques/article/view/396448
DOI: 10.5565/PUBLMAT6612210

33 p, 494.5 KB

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