Elliptic curves and ℤ p -extensions
Rubin, Karl
Compositio Mathematica, Tome 56 (1985), p. 237-250 / Harvested from Numdam
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Publié le : 1985-01-01
@article{CM_1985__56_2_237_0,
     author = {Rubin, Karl},
     title = {Elliptic curves and $\mathbb {Z}\_p$-extensions},
     journal = {Compositio Mathematica},
     volume = {56},
     year = {1985},
     pages = {237-250},
     mrnumber = {809869},
     zbl = {0599.14028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1985__56_2_237_0}
}

Rubin, Karl. Elliptic curves and $\mathbb {Z}_p$-extensions. Compositio Mathematica, Tome 56 (1985) pp. 237-250. http://gdmltest.u-ga.fr/item/CM_1985__56_2_237_0/

[1] D. Bertrand: Probèmes arithmétiques liés à 1'exponentielle p-adique sur les courbes elliptiques. C.R. Acad. Sci. Paris Sér. A 282, (1976) 1399-1401. | MR 414497 | Zbl 0331.14014

[2] J.W.S. Cassels: Arithmetic on curves of genus 1 (VII). J. Reine Angew. Math. 216 (1964) 150-158. | MR 169849 | Zbl 0146.42304

[3] J.W.S. Cassels: Arithmetic on curves of genus 1 (VIII). J. Reine Angew. Math. 217 (1965) 180-199. | MR 179169 | Zbl 0241.14017

[4] J. Coates: Infinite descent on elliptic curves with complex multiplication. In: Progress in Math. Vol. 35, pp. 107-138 Boston: Birkhauser (1983). | MR 717591 | Zbl 0541.14026

[5] J. Coates and A. Wiles: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math. 39 (1977) 223-251. | MR 463176 | Zbl 0359.14009

[6] R. Greenberg: On the structure of certain Galois groups. Invent. math. 47 (1978) 85-99. | MR 504453 | Zbl 0403.12004

[7] R. Greenberg: On the Birch and Swinnerton-Dyer conjecture. To appear. | MR 700770 | Zbl 0546.14015

[8] B. Gross and D. Zagier: To appear.

[9] G. Hochschild and J.-P. Serre: Cohomology of group extensions, Trans. Amer. Math. Soc. 74 (1953) 110-134. | MR 52438 | Zbl 0050.02104

[10] G. Konovalov: The universal G-norms of formal groups over a local field. Ukranian Math. J. 28 (1976) and 3 (1977) 310-311. | MR 439853 | Zbl 0345.14015

[11] E. Lutz: Sur 1'equation y2 = x3 - Ax - B dans les corps p-adiques. J. Reine Angew. Math. 177 (1977) 237-247. | JFM 63.0101.01 | Zbl 0017.05307

[12] D. Rohrlich: On L-functions of elliptic curves and anticyclotomic towers. To appear. | MR 735332 | Zbl 0565.14008

[13] D. Rohrlich: On L-functions of elliptic curves and cyclotomic towers. To appear. | MR 735333 | Zbl 0565.14006

[14] K. Rubin: On the arithmetic of CM elliptic curves in Zp-extensions. Thesis, Harvard University (1980).

[15] K. Rubin Elliptic Curves with complex multiplication and the conjecture of Birch and Swinnerton-dyer. Invent. Math. 64, (1981) 455-470. | MR 632985 | Zbl 0506.14039

[16] K. Rubin and A. Wiles: Mordell-Weil groups of elliptic curves over cyclotomic fields. In: Number Theory related to Fermat's last Theorem. Boston: Birkhauser (1982). | MR 685299 | Zbl 0519.14017

[17] J. Tate: Duality theorems in Galois cohomology over number fields. Proc. Internat. Congress Math. Stockholm 1962, pp. 288-295. | MR 175892 | Zbl 0126.07002

[18] M. Bashmakov: The cohomology of abelian varieties over a number field, Russian Math. Surveys 27 (1972) 25-70 | Zbl 0271.14010