Book Review
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MathSciNet review:
1567840
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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.
Max Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197–272 (German). MR 5125, DOI 10.1007/BF02940746
G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), no. 3, 349–366 (German). MR 718935, DOI 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)
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
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
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
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
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.
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, Mathematical Society of Japan, Tokyo, 1961. MR 0125113
Yutaka Taniyama, $L$-functions of number fields and zeta functions of abelian varieties, J. Math. Soc. Japan 9 (1957), 330–366. MR 95161, DOI 10.2969/jmsj/00930330
10. A. Weil, Courbes algébriques et variétés abéliennes (réimpression), Hermann, Paris, 1971.
- 1.
- M. Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hans. Univ. 14 (1941), 197-272. MR 0005125
- 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
