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ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Book Information:

Author: Jean-Pierre Serre
Title: Abelian $l$-adic representations and elliptic curves
Additional book information: Addison-Wesley Publ. Co., Reading, Mass., 1989, 140 pp., ISBN 0-201-09384-7.

References [Enhancements On Off] (What's this?)

  • 1. M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hans. Univ. 14 (1941), 197-272. MR 5125
  • 2. G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math 73 (1983), 349-366. English transl. Arithmetic Geometry, (G. Cornell and J. H. Silverman, eds. ), Springer-Verlag, Berlin and New York, 1986. MR 718935
  • 3. H. Hasse, Zur Theorie des abstrakten elliptischen Funktionenkörper. I-III, J. Reine Angew. Math. 175 55-62, 69-88, 193-208 (1936). (=Mathematische Abhandlungen 2, 223-266)
  • 4. R. P. Langlands, Automorphic representations, Shimura varieties, and motives, Ein Märchen. Proc. Sympos. Pure Math., vol. 33(2), Amer. Math. Soc., Providence, R.I., 1979, pp. 205-246. MR 546619
  • 5. D. Mumford, Families of Abelian varieties, Proc. Sympos. Pure Math., vol. 9, Amer. Math. Soc., Providence, R.I., 1966, pp. 347-351. MR 206003
  • 6. P. Deligne, J. S. Milne, A. Ogus and K-y. Shih, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Math., vol. 900, Springer-Verlag, Berlin and New York, 1982. MR 654325
  • 7. J.-P. Serre, Représentations l-adiques, Algebraic Number Theory (International Symposium, Kyoto 1976) (S. Iyanaga, ed.), Tokyo: Japanese Society for the Promotion of Science, 1977. MR 476753
  • 8. J.-P. Serre, Groupes algébriques associés aux modules de Hodge-Tate, Astérisque 65 (1979), 155-188. MR 563476
  • 9. J.-P. Serre, Course at the Collège de France, 1984-1985.
  • 10. G. Shimura and Y. Taniyama, Complex multiplication of Abelian varieties and its applications to number theory, Tokyo: The Mathematical Society of Japan, 1961. MR 125113
  • 11. Y. Taniyama, L-functions of number fields and zeta functions of abelian varieties, J. Math. Soc. Japan 9 (1957), 330-366. MR 95161
  • 10. A. Weil, Courbes algébriques et variétés abéliennes (réimpression), Hermann, Paris, 1971.

Review Information:

Reviewer: Kenneth A. Ribet
Journal: Bull. Amer. Math. Soc. 22 (1990), 214-218
DOI: https://doi.org/10.1090/S0273-0979-1990-15882-3
American Mathematical Society