×
Coates, J.; Wiles, A.

On the conjecture of Birch and Swinnerton-Dyer. (English) Zbl 0359.14009

Invent. Math. 39, 223-251 (1977).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0359.14009

Cited in 21 Reviews
Cited in 117 Documents

MSC:

14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14H45 Special algebraic curves and curves of low genus
14H25 Arithmetic ground fields for curves
14G25 Global ground fields in algebraic geometry
11G15 Complex multiplication and moduli of abelian varieties
11R42 Zeta functions and \(L\)-functions of number fields
PDF BibTeX XML Cite
\textit{J. Coates} and \textit{A. Wiles}, Invent. Math. 39, 223--251 (1977; Zbl 0359.14009)
Full Text: DOI EuDML

References:

[1] Artin, E., Tate, J.: Class field theory. New York: Benjamin 1967 · Zbl 1179.11040
[2] Birch, B., Swinnerton-Dyer, P.: Notes on elliptic curves II. J. Reine Angew. Math.218, 79-108 (1965) · Zbl 0147.02506
[3] Coates, J., Wiles, A.: Kummer’s criterion for Hurwitz numbers, to appear in Proceedings of the International Conference on Algebraic Number Theory held in Kyoto, Japan, 1976 · Zbl 0369.12009
[4] Damerell, R.:L-functions of elliptic curves with complex multiplication I. Acta Arith.17, 287-301 (1970) · Zbl 0209.24603
[5] Deuring, D.: Die Zetafunktionen einer algebraischen Kurve vom Geschlechter Eins, I, II, III, IV. Nachr. Akad. Wiss. Göttingen, 85-94 (1953); 13-42 (1955); 37-76 (1956); 55-80 (1957) · Zbl 0064.27401
[6] Fröhlich, A.: Formal Groups. Lecture Notes in Math.74. Berlin-Heidelberg-New York: Springer 1968 · Zbl 0177.04801
[7] Hasse, H.: Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil II, 2nd ed. Würzburg-Wien: Physica 1965 · Zbl 0138.03202
[8] Iwasawa, K.: On some modules in the theory of cyclotomic fields. J. Math. Soc. Japan,16, 42-82 (1964) · Zbl 0125.29207
[9] Lubin, J.: One parameter formal Lie groups overp-adic integer rings. Ann. of Math.80, 464-484 (1964) · Zbl 0135.07003
[10] Lubin, J., Tate, J.: Formal complex multiplication in local fields. Ann. Math.81, 380-387 (1965) · Zbl 0128.26501
[11] Mazur, B.: Rational points of abelian varieties with values in towers of number fields. Inventiones math.18, 183-266 (1972) · Zbl 0245.14015
[12] Robert, G.: Unités elliptiques. Bull. Soc. Math. France, Mémoire36, 1973
[13] Robert, G.: Nombres de Hurwitz et Unités elliptiques. To appear
[14] Sah, H.: Automorphisms of finite groups. J. Algebra10, 47-68 (1968) · Zbl 0159.31001
[15] Serre, J.P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492-517 (1968) · Zbl 0172.46101
[16] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Pub. Math. Soc. Japan,11, 1971 · Zbl 0221.10029
[17] Tate, J.: Algorithm for determining the type of a singular fiber in an elliptic pencil. In: Modular functions of one variable IV. Lecture Notes in Math.476. Berlin-Heidelberg-New York: Springer 1975 · Zbl 1214.14020
[18] Wiles, A.: Higher explicit reciprocity laws. To appear · Zbl 0378.12006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.