Elliptic curves and ℤ p -extensions

Karl Rubin

Compositio Mathematica (1985)

  • Volume: 56, Issue: 2, page 237-250
  • ISSN: 0010-437X

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Rubin, Karl. "Elliptic curves and $\mathbb {Z}_p$-extensions." Compositio Mathematica 56.2 (1985): 237-250. <http://eudml.org/doc/89739>.

@article{Rubin1985,
author = {Rubin, Karl},
journal = {Compositio Mathematica},
keywords = {elliptic curve; complex multiplication; Mordell-Weil group; Tate- Shafarevich group; Iwasawa theory},
language = {eng},
number = {2},
pages = {237-250},
publisher = {Martinus Nijhoff Publishers},
title = {Elliptic curves and $\mathbb \{Z\}_p$-extensions},
url = {http://eudml.org/doc/89739},
volume = {56},
year = {1985},
}

TY - JOUR
AU - Rubin, Karl
TI - Elliptic curves and $\mathbb {Z}_p$-extensions
JO - Compositio Mathematica
PY - 1985
PB - Martinus Nijhoff Publishers
VL - 56
IS - 2
SP - 237
EP - 250
LA - eng
KW - elliptic curve; complex multiplication; Mordell-Weil group; Tate- Shafarevich group; Iwasawa theory
UR - http://eudml.org/doc/89739
ER -

References

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  1. [1] D. Bertrand: Probèmes arithmétiques liés à 1'exponentielle p-adique sur les courbes elliptiques. C.R. Acad. Sci. Paris Sér. A282, (1976) 1399-1401. Zbl0331.14014MR414497
  2. [2] J.W.S. Cassels: Arithmetic on curves of genus 1 (VII). J. Reine Angew. Math.216 (1964) 150-158. Zbl0146.42304MR169849
  3. [3] J.W.S. Cassels: Arithmetic on curves of genus 1 (VIII). J. Reine Angew. Math.217 (1965) 180-199. Zbl0241.14017MR179169
  4. [4] J. Coates: Infinite descent on elliptic curves with complex multiplication. In: Progress in Math. Vol. 35, pp. 107-138Boston: Birkhauser (1983). Zbl0541.14026MR717591
  5. [5] J. Coates and A. Wiles: On the conjecture of Birch and Swinnerton-Dyer. Invent. Math.39 (1977) 223-251. Zbl0359.14009MR463176
  6. [6] R. Greenberg: On the structure of certain Galois groups. Invent. math.47 (1978) 85-99. Zbl0403.12004MR504453
  7. [7] R. Greenberg: On the Birch and Swinnerton-Dyer conjecture. To appear. Zbl0546.14015MR700770
  8. [8] B. Gross and D. Zagier: To appear. 
  9. [9] G. Hochschild and J.-P. Serre: Cohomology of group extensions, Trans. Amer. Math. Soc.74 (1953) 110-134. Zbl0050.02104MR52438
  10. [10] G. Konovalov: The universal G-norms of formal groups over a local field. Ukranian Math. J.28 (1976) and 3 (1977) 310-311. Zbl0345.14015MR439853
  11. [11] E. Lutz: Sur 1'equation y2 = x3 - Ax - B dans les corps p-adiques. J. Reine Angew. Math.177 (1977) 237-247. Zbl0017.05307JFM63.0101.01
  12. [12] D. Rohrlich: On L-functions of elliptic curves and anticyclotomic towers. To appear. Zbl0565.14008MR735332
  13. [13] D. Rohrlich: On L-functions of elliptic curves and cyclotomic towers. To appear. Zbl0565.14006MR735333
  14. [14] K. Rubin: On the arithmetic of CM elliptic curves in Zp-extensions. Thesis, Harvard University (1980). 
  15. [15] K. RUBIN Elliptic curveswith complex multiplication and the conjecture of Birch and Swinnerton-dyer. Invent. Math.64, (1981) 455-470. Zbl0506.14039MR632985
  16. [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). Zbl0519.14017MR685299
  17. [17] J. Tate: Duality theorems in Galois cohomology over number fields. Proc. Internat. Congress Math. Stockholm 1962, pp. 288-295. Zbl0126.07002MR175892
  18. [18] M. Bashmakov: The cohomology of abelian varieties over a number field, Russian Math. Surveys27 (1972) 25-70 Zbl0271.14010

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