Elliptic curves and p -extensions

Karl Rubin

Compositio Mathematica (1985)

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

How to cite


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

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},

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 -


  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

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.