Review: Ph. Cassou-Noguès and M. J. Taylor, Elliptic functions and rings of integers
Ted Chinburg
Source: Bull. Amer. Math. Soc. (N.S.) Volume 20, Number 1
(1989), 117-121.
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Ph. Cassou-Noguès, M. J. Taylor, Elliptic functions and rings of integers. Progress in Mathematics, vol. 66, Birkhäuser, Boston, Basel and Stuttgart, 1987, xvi + 198 pp., $29.50. ISBN 0-8176-3350-2
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Permanent link to this document: http://projecteuclid.org/euclid.bams/1183554919
References
1. J. Brinkhuis, Galois modules and embedding problems, J. Reine Angew. Math. 346 (1984), 141-165.
Zentralblatt MATH: 0525.12008
Mathematical Reviews (MathSciNet): MR727401
2. J. Brinkhuis, Normal integral bases and complex conjugation, J. Reine Angew. Math. 375/376 (1987), 157-166.
Zentralblatt MATH: 0609.12009
Mathematical Reviews (MathSciNet): MR882295
3. Ph. Cassou-Noguès and M. J. Taylor, A note on elliptic curves and the monogeneity of rings of integers, J. London Math. Soc. (2) 37 (1988), 63-72.
Zentralblatt MATH: 0639.12001
Mathematical Reviews (MathSciNet): MR921747
4. J. Cougnard, Conditions nécessaires de monogénéité, application aux extensions cycliques de degré premier l ≥ 5 d'un corps quadratique imaginaire, J. London Math. Soc. (2) 37 (1988), 73-87.
Zentralblatt MATH: 0647.12002
Mathematical Reviews (MathSciNet): MR921746
Digital Object Identifier: doi:10.1112/jlms/s2-37.121.73
5. A. Fröhlich, Galois module structure of algebraic integers, Ergebnisse 3 Folge Band I, Springer-Verlag, Berlin and New York, 1983.
Zentralblatt MATH: 0501.12012
Mathematical Reviews (MathSciNet): MR717033
6. M. N. Gras, Non-monogénéite de l'anneau des entiers des extensions cycliques de Q de degré premier l ≥ 5, J. Number Theory 23 (1986), 347-353.
Zentralblatt MATH: 0582.12003
Mathematical Reviews (MathSciNet): MR846964
Digital Object Identifier: doi:10.1016/0022-314X(86)90079-X
7. D. Hilbert, Mathematical problems, Lecture delivered at the International Congress of Mathematicians in Paris in 1900, Bull. Amer. Math. Soc. 8 (1902), 437-479.
Mathematical Reviews (MathSciNet): MR1557926
Digital Object Identifier: doi:10.1090/S0002-9904-1902-00923-3
Project Euclid: euclid.bams/1183417035
8. L. Kronecker, Werke, Band V, (K. Hensel ed.), Teubner, Leipzig and Berlin, 1930.
9. R. Langlands, Automorphic representations, Shimura varieties and motives. Ein Märchen, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, R. I., 1979, pp. 205-246.
Zentralblatt MATH: 0447.12009
Mathematical Reviews (MathSciNet): MR546619
10. R. Langlands, Some contemporary problems with origins in the Jugendtraum, Proc. Sympos. Pure Math., vol. 28, Amer. Math. Soc. Providence, R. I., 1976, pp. 401-418.
Zentralblatt MATH: 0345.14006
Mathematical Reviews (MathSciNet): MR437500
11. H. W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math. 201 (1959), 119-149.
Zentralblatt MATH: 0098.03403
Mathematical Reviews (MathSciNet): MR108479
12. L. McCulloh, Galois module structure of abelian extensions, J. Reine Angew. Math. 375/376 (1987), 259-306.
Zentralblatt MATH: 0619.12008
Mathematical Reviews (MathSciNet): MR882300
13. J. Milne, Automorphic bundles on connected Shimura varieties, Invent. Math. 92 (1988), 91-128.
Zentralblatt MATH: 0684.14006
Mathematical Reviews (MathSciNet): MR931206
Digital Object Identifier: doi:10.1007/BF01393994
14. G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press, Princeton, N.J., 1971.
Zentralblatt MATH: 0221.10029
Mathematical Reviews (MathSciNet): MR314766
15. H. M. Stark, Hilbert's twelfth problem and L-series, Bull. Amer. Math. Soc. 83 (1977), 1072-1074.
Zentralblatt MATH: 0378.12007
Mathematical Reviews (MathSciNet): MR441923
Digital Object Identifier: doi:10.1090/S0002-9904-1977-14389-9
Project Euclid: euclid.bams/1183539485
16. H. M. Stark, L-functions at s = 1. III. Totally real fields and Hilbert's Twelfth Problem, Adv. in Math. 22 (1976), 64-84.
Zentralblatt MATH: 0348.12017
Mathematical Reviews (MathSciNet): MR437501
Digital Object Identifier: doi:10.1016/0001-8708(76)90138-9
17. H. M. Stark, L-functions at s = 1. IV. First derivatives at s = 0, Adv. in Math. 35 (1980), 197-235.
Zentralblatt MATH: 0475.12018
Mathematical Reviews (MathSciNet): MR563924
Digital Object Identifier: doi:10.1016/0001-8708(80)90049-3
18. J. Tate, Les Conjectures de Stark sur les fonctions L d'Artin en s = 0, Notes d'un cours à Orsay rédigées par D. Bernardi et N. Schappacher, Birkhäuser, Boston, Basel, Stuttgart, 1984.
Zentralblatt MATH: 0545.12009
Mathematical Reviews (MathSciNet): MR782485
19. M. J. Taylor, Formal groups and the Galois module structure of local rings of integers, J. Reine Angew. Math. 358 (1985), 97-103.
Zentralblatt MATH: 0582.12008
Mathematical Reviews (MathSciNet): MR797677
20. M. J. Taylor, Mordell-Weil groups and the Galois module structure of rings of integers, Illinois J. Math. (to appear).
Zentralblatt MATH: 0631.14033
Mathematical Reviews (MathSciNet): MR947037
Project Euclid: euclid.ijm/1255988996
21. M. J. Taylor, Relative Galois module structure of rings of integers and elliptic functions, Math. Proc Cambridge Philos. Soc. 94 (1983), 389-397; II, Ann. of Math. (2) 121 (1985), 519-535; III, Proc. London Math. Soc. (3) 51 (1985), 415-431.
Zentralblatt MATH: 0578.12004
Mathematical Reviews (MathSciNet): MR720789
Digital Object Identifier: doi:10.1017/S0305004100000773
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