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Bulletin of the American Mathematical Society

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

Book Review

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Full text of review: PDF
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. Max Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197–272 (German). MR 0005125
  • 2. G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), no. 3, 349–366 (German). MR 718935, 10.1007/BF01388432
  • 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, Automorphic forms, representations and 𝐿-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 205–246. MR 546619
  • 5. David Mumford, Families of abelian varieties, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 347–351. MR 0206003
  • 6. Pierre Deligne, James S. Milne, Arthur Ogus, and Kuang-yen Shih, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin-New York, 1982. MR 654325
  • 7. Jean-Pierre Serre, Représentations 𝑙-adiques, Algebraic number theory (Kyoto Internat. Sympos., Res. Inst. Math. Sci., Univ. Kyoto, Kyoto, 1976) Japan Soc. Promotion Sci., Tokyo, 1977, pp. 177–193 (French). MR 0476753
  • 8. Jean-Pierre Serre, Groupes algébriques associés aux modules de Hodge-Tate, Journées de Géométrie Algébrique de Rennes. (Rennes, 1978) Astérisque, vol. 65, Soc. Math. France, Paris, 1979, pp. 155–188 (French). MR 563476
  • 9. J.-P. Serre, Course at the Collège de France, 1984-1985.
  • 10. 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. MR 0125113
  • 11. Yutaka Taniyama, 𝐿-functions of number fields and zeta functions of abelian varieties., J. Math. Soc. Japan 9 (1957), 330–366. MR 0095161
  • 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: http://dx.doi.org/10.1090/S0273-0979-1990-15882-3