On the structure of the Iwasawa module for Z2-extensions of certain real biquadratic fields

被引：0
作者：
El Mahi, A. [1 ]
机构：
[1] Fac Sci, Oujda, Morocco
来源：
ACTA MATHEMATICA HUNGARICA | 2024年 / 174卷 / 01期
关键词：
Iwasawa theory; Z(2)-extension; real biquadratic field; 2-class group; class field theory; unit; CYCLOTOMIC Z(2)-EXTENSION; LAMBDA-INVARIANT; Q(ROOT-P); IDEALS;
D O I：
10.1007/s10474-024-01459-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For an infinite family of real biquadratic fields k we give the structure of the Iwasawa module X = X(k(infinity)) of the Z(2)-extension of k. For these fields, we obtain that lambda = mu = 0 and nu = 2. where lambda, mu and nu are the Iwasawa invariants of the cyclotomic Z(2)-extension of k.
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页码：49 / 61
页数：13
相关论文
共 20 条
[1]  
El Mahi A, 2021, ACTA MATH HUNG, V165, P146, DOI 10.1007/s10474-021-01174-2
[2]   IWASAWA INVARIANT MU-P VANISHES FOR ABELIAN NUMBER FIELDS [J].
FERRERO, B ;
WASHINGTON, LC .
ANNALS OF MATHEMATICS, 1979, 109 (02) :377-395
[3]   REMARKS OF Z(P)-EXTENSIONS OF NUMBER-FIELDS [J].
FUKUDA, T .
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1994, 70 (08) :264-266
[4]   ON THE IWASAWA lambda-INVARIANT OF THE CYCLOTOMIC Z(2)-EXTENSION OF Q(root p) II [J].
Fukuda, Takashi ;
Komatsu, Keiichi .
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2014, 51 (01) :167-179
[5]   ON THE IWASAWA lambda-INVARIANT OF THE CYCLOTOMIC Z(2)-EXTENSION OF Q(root p), III [J].
Fukuda, Takashi ;
Komatsu, Keiichi ;
Ozaki, Manabu ;
Tsuji, Takae .
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2016, 54 (01) :7-17
[6]  
Gorensten D., 1980, FINITE GROUPS
[7]  
GRAS G, 1973, ANN I FOURIER, V23, P1
[8]   IWASAWA INVARIANTS OF TOTALLY REAL NUMBER FIELDS [J].
GREENBERG, R .
AMERICAN JOURNAL OF MATHEMATICS, 1976, 98 (01) :263-284
[9]  
Hasse H, 1930, J REINE ANGEW MATH, V162, P134
[10]  
Kaplan P., 1976, J. Reine Angew. Math., P313
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