Bulletin of the American Mathematical Society

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Book Information:

Authors: Ph. Cassou-Noguès and M. J. Taylor
Title: Elliptic functions and rings of integers
Additional book information: Progress in Mathematics, vol. 66, Birkhäuser, Boston, Basel and Stuttgart, 1987, xvi + 198 pp., $29.50. ISBN 0-8176-3350-2.

Jan Brinkhuis, Galois modules and embedding problems, J. Reine Angew. Math. 346 (1984), 141–165. MR 727401, DOI 10.1515/crll.1984.346.141

Jan Brinkhuis, Normal integral bases and complex conjugation, J. Reine Angew. Math. 375/376 (1987), 157–166. MR 882295, DOI 10.1515/crll.1987.375-376.157

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), no. 1, 63–72. MR 921747, DOI 10.1112/jlms/s2-37.121.63

Jean Cougnard, Conditions nécessaires de monogénéité. Application aux extensions cycliques de degré premier $l\geq 5$ d’un corps quadratique imaginaire, J. London Math. Soc. (2) 37 (1988), no. 1, 73–87 (French). MR 921746, DOI 10.1112/jlms/s2-37.121.73

Albrecht Fröhlich, Galois module structure of algebraic integers, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 1, Springer-Verlag, Berlin, 1983. MR 717033, DOI 10.1007/978-3-642-68816-4

Marie-Nicole Gras, Non monogénéité de l’anneau des entiers des extensions cycliques de $\textbf {Q}$ de degré premier $l\geq 5$, J. Number Theory 23 (1986), no. 3, 347–353 (French, with English summary). MR 846964, 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.

8.

L. Kronecker, Werke, Band V, (K. Hensel ed. ), Teubner, Leipzig and Berlin, 1930.

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

R. P. Langlands, Some contemporary problems with origins in the Jugendtraum, Mathematical developments arising from Hilbert problems (Proc. Sympos. Pure Math., Northern Illinois Univ., De Kalb, Ill., 1974) Amer. Math. Soc., Providence, R.I., 1976, pp. 401–418. MR 0437500

Heinrich-Wolfgang Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math. 201 (1959), 119–149 (German). MR 108479, DOI 10.1515/crll.1959.201.119

Leon R. McCulloh, Galois module structure of abelian extensions, J. Reine Angew. Math. 375/376 (1987), 259–306. MR 882300, DOI 10.1515/crll.1987.375-376.259

J. S. Milne, Automorphic vector bundles on connected Shimura varieties, Invent. Math. 92 (1988), no. 1, 91–128. MR 931206, DOI 10.1007/BF01393994

Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766

H. M. Stark, Hilbert’s twelfth problem and $L$-series, Bull. Amer. Math. Soc. 83 (1977), no. 5, 1072–1074. MR 441923, DOI 10.1090/S0002-9904-1977-14389-9

H. M. Stark, $L$-functions at $s=1$. III. Totally real fields and Hilbert’s twelfth problem, Advances in Math. 22 (1976), no. 1, 64–84. MR 437501, DOI 10.1016/0001-8708(76)90138-9

Harold M. Stark, $L$-functions at $s=1$. IV. First derivatives at $s=0$, Adv. in Math. 35 (1980), no. 3, 197–235. MR 563924, DOI 10.1016/0001-8708(80)90049-3

John Tate, Les conjectures de Stark sur les fonctions $L$ d’Artin en $s=0$, Progress in Mathematics, vol. 47, Birkhäuser Boston, Inc., Boston, MA, 1984 (French). Lecture notes edited by Dominique Bernardi and Norbert Schappacher. MR 782485

M. J. Taylor, Formal groups and the Galois module structure of local rings of integers, J. Reine Angew. Math. 358 (1985), 97–103. MR 797677, DOI 10.1515/crll.1985.358.97

M. J. Taylor, Mordell-Weil groups and the Galois module structure of rings of integers, Illinois J. Math. 32 (1988), no. 3, 428–452. MR 947037

M. J. Taylor, Relative Galois module structure of rings of integers and elliptic functions, Math. Proc. Cambridge Philos. Soc. 94 (1983), no. 3, 389–397. MR 720789, DOI 10.1017/S0305004100000773

1.

J. Brinkhuis, Galois modules and embedding problems, J. Reine Angew. Math. 346 (1984), 141-165. MR 0727401

2.

J. Brinkhuis, Normal integral bases and complex conjugation, J. Reine Angew. Math. 375/376 (1987), 157-166. MR 882295

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. MR 921747

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. MR 921746

5.

A. Fröhlich, Galois module structure of algebraic integers, Ergebnisse 3 Folge Band I, Springer-Verlag, Berlin and New York, 1983. MR 717033

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. MR 846964

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.

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. MR 546619

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. MR 437500

11.

H. W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine Angew. Math. 201 (1959), 119-149. MR 108479

12.

L. McCulloh, Galois module structure of abelian extensions, J. Reine Angew. Math. 375/376 (1987), 259-306. MR 882300

13.

J. Milne, Automorphic bundles on connected Shimura varieties, Invent. Math. 92 (1988), 91-128. MR 931206

14.

G. Shimura, Introduction to the arithmetic theory of automorphic functions, Iwanami Shoten and Princeton Univ. Press, Princeton, N.J., 1971. MR 314766

15.

H. M. Stark, Hilbert's twelfth problem and L-series, Bull. Amer. Math. Soc. 83 (1977), 1072-1074. MR 441923

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. MR 437501

17.

H. M. Stark, L-functions at s = 1. IV. First derivatives at s = 0, Adv. in Math. 35 (1980), 197-235. MR 563924

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. MR 782485

19.

M. J. Taylor, Formal groups and the Galois module structure of local rings of integers, J. Reine Angew. Math. 358 (1985), 97-103. MR 797677

20.

M. J. Taylor, Mordell-Weil groups and the Galois module structure of rings of integers, Illinois J. Math. (to appear). MR 947037

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. MR 720789