Division fields of abelian varieties with complex multiplication

K. A. Ribet

Mémoires de la Société Mathématique de France (1980)

  • Volume: 2, page 75-94
  • ISSN: 0249-633X

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Ribet, K. A.. "Division fields of abelian varieties with complex multiplication." Mémoires de la Société Mathématique de France 2 (1980): 75-94. <http://eudml.org/doc/94824>.

@article{Ribet1980,
author = {Ribet, K. A.},
journal = {Mémoires de la Société Mathématique de France},
keywords = {Abelian varieties with complex multiplication; Serre-Tate modules; algebraic tori},
language = {eng},
pages = {75-94},
publisher = {Société mathématique de France},
title = {Division fields of abelian varieties with complex multiplication},
url = {http://eudml.org/doc/94824},
volume = {2},
year = {1980},
}

TY - JOUR
AU - Ribet, K. A.
TI - Division fields of abelian varieties with complex multiplication
JO - Mémoires de la Société Mathématique de France
PY - 1980
PB - Société mathématique de France
VL - 2
SP - 75
EP - 94
LA - eng
KW - Abelian varieties with complex multiplication; Serre-Tate modules; algebraic tori
UR - http://eudml.org/doc/94824
ER -

References

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  2. [2] Greenberg, R., On the Jacobian variety of some algebraic curves. Preprint, 1978. 
  3. [3] Koblitz, N. and Rohrlich, N., Simple factors in the Jacobian of a Fermat curve. Canadian J. Math. 30, 1183-1205 (1978). Zbl0399.14023MR80d:14022
  4. [4] Kubota, T., On the field extension by complex multiplication. Trans. AMS 118, n° 6, 113-122 (1965). Zbl0146.27902MR32 #7558
  5. [5] Lang, S., Algebraic groups over finite fields. Am. J. Math 78, 555-563 (1956). Zbl0073.37901MR19,174a
  6. [6] Masser, D. W., On quasi-periods of abelian functions with complex multiplication. This volume. Zbl0444.10027
  7. [7] Ono, T., Arithmetic of algebraic tori. Ann. of Math. 74, 101-139 (1961). Zbl0119.27801MR23 #A1640
  8. [8] Ono, T., On the Tamagawa number of algebraic tori. Ann. of Math. 78, 47-73 (1963). Zbl0122.39101MR28 #94
  9. [9] Pohlmann, H., Algebraic cycles on abelian varieties of complex multiplication type. Ann. of Math. 88, 161-180 (1968). Zbl0201.23201MR37 #4080
  10. [10] Ribet, K.A., Kummer theory on extensions of abelian varieties by tori. Duke Math. J. 46, 745-761 (1979). Zbl0428.14018MR81g:14019
  11. [11] Serre, J. P., Groupes Algébriques et Corps de Classes. Hermann, Paris, 1959. Zbl0097.35604MR21 #1973
  12. [12] Serre, J. P., Corps Locaux. Deuxième édition revue et corrigée. Hermann, Paris, 1968. Zbl0137.02601MR50 #7096
  13. [13] Serre, J. P., Letter to D. Masser, November, 1975. 
  14. [14] Serre, J.P., Représentations l-adiques. In Algebraic Number Theory (Int. Symp., Kyoto, 1976), Japan Society for the Promotion of Science, Tokyo, 1977. Zbl0406.14015
  15. [15] Serre, J.P. and Tate, J., Good reduction of abelian varieties. Ann. of Math. 88, 492-517 (1968). Zbl0172.46101MR38 #4488
  16. [16] Shimura, G., Arithmetic quotients of bounded symmetric domains. Ann. of Math. 91, 144-222 (1970). Zbl0237.14009MR41 #1686
  17. [17] Shimura, G. and Taniyama, Y., Complex Multiplication of Abelian Varieties and its Applications to Number Theory. Publ. Math. Soc. Japan n° 6, Tokyo, 1961. Zbl0112.03502MR23 #A2419
  18. [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]. Zbl0073.26303MR18,720e

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