Ribet, K. A. Division fields of Abelian varieties with complex multiplication. (English) Zbl 0452.14009 Mém. Soc. Math. Fr., Nouv. Sér. 2, 75-94 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 23 Documents MSC: 14K22 Complex multiplication and abelian varieties 14K15 Arithmetic ground fields for abelian varieties 14G25 Global ground fields in algebraic geometry 11R18 Cyclotomic extensions Keywords:Abelian varieties with complex multiplication; Serre-Tate modules; algebraic tori PDF BibTeX XML Cite \textit{K. A. Ribet}, Mém. Soc. Math. Fr., Nouv. Sér. 2, 75--94 (1980; Zbl 0452.14009) Full Text: DOI Numdam EuDML References: [1] Deligne, P. , Cycles de Hodge absolus et périodes des intégrales des variétés abéliennes , rédigé par J. L. Brylinski. This volume. Numdam | Zbl 0453.14020 · Zbl 0453.14020 · numdam:MSMF_1980_2_2__23_0 · eudml:94815 [2] Greenberg, R. , On the Jacobian variety of some algebraic curves . Preprint, 1978 . [3] Koblitz, N. and Rohrlich, N. , Simple factors in the Jacobian of a Fermat curve . Canadian J. Math. 30, 1183-1205 ( 1978 ). MR 80d:14022 | Zbl 0399.14023 · Zbl 0399.14023 · doi:10.4153/CJM-1978-099-6 [4] Kubota, T. , On the field extension by complex multiplication. Trans. AMS 118, n^\circ 6, 113-122 ( 1965 ). MR 32 #7558 | Zbl 0146.27902 · Zbl 0146.27902 · doi:10.2307/1993947 [5] Lang, S. , Algebraic groups over finite fields . Am. J. Math 78, 555-563 ( 1956 ). MR 19,174a | Zbl 0073.37901 · Zbl 0073.37901 · doi:10.2307/2372673 [6] Masser, D. W. , On quasi-periods of abelian functions with complex multiplication . This volume. Numdam | Zbl 0444.10027 · Zbl 0444.10027 · numdam:MSMF_1980_2_2__55_0 · eudml:94819 [7] Ono, T. , Arithmetic of algebraic tori . Ann. of Math. 74, 101-139 ( 1961 ). MR 23 #A1640 | Zbl 0119.27801 · Zbl 0119.27801 · doi:10.2307/1970307 [8] Ono, T. , On the Tamagawa number of algebraic tori . Ann. of Math. 78, 47-73 ( 1963 ). MR 28 #94 | Zbl 0122.39101 · Zbl 0122.39101 · doi:10.2307/1970502 [9] Pohlmann, H. , Algebraic cycles on abelian varieties of complex multiplication type . Ann. of Math. 88, 161-180 ( 1968 ). MR 37 #4080 | Zbl 0201.23201 · Zbl 0201.23201 · doi:10.2307/1970570 [10] Ribet, K.A. , Kummer theory on extensions of abelian varieties by tori . Duke Math. J. 46, 745-761 ( 1979 ). Article | MR 81g:14019 | Zbl 0428.14018 · Zbl 0428.14018 · doi:10.1215/S0012-7094-79-04638-6 · minidml.mathdoc.fr [11] Serre, J. P. , Groupes Algébriques et Corps de Classes . Hermann, Paris, 1959 . MR 21 #1973 | Zbl 0097.35604 · Zbl 0097.35604 [12] Serre, J. P. , Corps Locaux . Deuxième édition revue et corrigée. Hermann, Paris, 1968 . MR 50 #7096 | Zbl 0137.02601 · Zbl 0137.02601 [13] Serre, J. P. , Letter to D. Masser , November, 1975 . [14] Serre, J.P. , Représentations l-adiques . In Algebraic Number Theory (Int. Symp., Kyoto, 1976 ), Japan Society for the Promotion of Science, Tokyo, 1977 . Zbl 0406.14015 · Zbl 0406.14015 [15] Serre, J.P. and Tate, J. , Good reduction of abelian varieties . Ann. of Math. 88, 492-517 ( 1968 ). MR 38 #4488 | Zbl 0172.46101 · Zbl 0172.46101 · doi:10.2307/1970722 [16] Shimura, G. , Arithmetic quotients of bounded symmetric domains . Ann. of Math. 91, 144-222 ( 1970 ). MR 41 #1686 | Zbl 0237.14009 · Zbl 0237.14009 · doi:10.2307/1970604 · www.jstor.org [17] Shimura, G. and Taniyama, Y. , Complex Multiplication of Abelian Varieties and its Applications to Number Theory . Publ. Math. Soc. Japan n^\circ 6, Tokyo, 1961 . MR 23 #A2419 | Zbl 0112.03502 · Zbl 0112.03502 [18] Weil, A. , On a certain type of characters of the idèle-class group of an algebraic number-field . Proc. International Symp. on Algebraic Number Theory, Tokyo-Nikko, 1-7 ( 1955 ) = Collected Papers [1955c]. MR 18,720e | Zbl 0073.26303 · Zbl 0073.26303 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.