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On the field extension by complex multiplication. (English) Zbl 0146.27902

MSC:
11R18 Cyclotomic extensions
11G15 Complex multiplication and moduli of abelian varieties
Keywords:
number theory
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References:
[1] Irving Kaplansky, Infinite abelian groups, University of Michigan Press, Ann Arbor, 1954. · Zbl 0057.01901
[2] Tomio Kubota, Galois group of the maximal abelian extension over an algebraic number field, Nagoya Math. J. 12 (1957), 177 – 189. · Zbl 0079.26803
[3] Heinrich-Wolfgang Leopoldt, Zur Arithmetik in abelschen Zahlk√∂rpern, J. Reine Angew. Math. 209 (1962), 54 – 71. · Zbl 0204.07101 · doi:10.1515/crll.1962.209.54 · doi.org
[4] Goro Shimura, On the class-fields obtained by complex multiplication of abelian varieties, Osaka Math. J. 14 (1962), 33 – 44. · Zbl 0116.02903
[5] Goro Shimura and Yutaka Taniyama, Complex multiplication of abelian varieties and its applications to number theory, Publications of the Mathematical Society of Japan, vol. 6, The Mathematical Society of Japan, Tokyo, 1961. · Zbl 0112.03502
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