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

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
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References:
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[2] Birch, B., Swinnerton-Dyer, P.: Notes on elliptic curves II. J. Reine Angew. Math.218, 79-108 (1965) · Zbl 0147.02506 · doi:10.1515/crll.1965.218.79
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[12] Robert, G.: Unités elliptiques. Bull. Soc. Math. France, Mémoire36, 1973
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[15] Serre, J.P., Tate, J.: Good reduction of abelian varieties. Ann. Math.88, 492-517 (1968) · Zbl 0172.46101 · doi:10.2307/1970722
[16] Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Pub. Math. Soc. Japan,11, 1971 · Zbl 0221.10029
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[18] Wiles, A.: Higher explicit reciprocity laws. To appear · Zbl 0378.12006
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