On the Iwasawa theory of CM elliptic curves at supersingular primes

 Access to full text

 Full (PDF)

1. [Bi] Billot, P.: Quelques aspects de la descente sur une courbe elliptique dans le cas de réduction supersingulière, Compos. Math.58 (1986), 341-369. Zbl0604.14017MR846910
2. [Bo] Bourbaki, N.: Commutative Algebra. Hermann, Paris1972. MR360549
3. [Ca] Cassels, J.W.S.: Arithmetic on curves of genus 1, IV, J. Reine und Angew. Math., 207 (1962), 234-246. Zbl0118.27701
4. [CGr] Coates, J. and Greenberg, R.: Kummer theory for abelian varieties over local fields, Inv. Math.124 (1996), 129-174. Zbl0858.11032MR1369413
5. [CMc] Coates, J. and McConnell, G.: On the Iwasawa theory of modular elliptic curves of analytic rank ≤ 1, to appear in Jnl. Lon. Math. Soc. Zbl0864.11053
6. [CW] Coates, J. and Wiles, A.: On the Conjecture of Birch and Swinnerton-Dyer, Inv. Math.39223-251 (1977). Zbl0359.14009MR463176
7. [deS] de Shalit, E.: Iwasawa theory for elliptic curves with complex multiplication, Perspectives in Mathematics3, Academic Press, Boston, 1987. Zbl0674.12004MR917944
8. [Gr1] Greenberg, R.: On the structure of certain Galois groups, Invent. Math.47 (1978), 85-99. Zbl0403.12004MR504453
9. [Gr2] Greenberg, R.: Non-vanishing of certain values of L-functions, in Analytic Number Theory and Diophantine Problems, proceedings of a conference at Oklahoma State University (1984), P.I.M. vol. 70, BirkhäuserBoston1987. Zbl0629.12010
10. [Gr3] Greenberg, R.: Iwasawa Theory for p-adic Representations, in Advanced Studies in Pure Math. 17, Kinokuniya & Academic Press (1989), 97-137. Zbl0739.11045MR1097613
11. [G] Gross, B.: Arithmetic on elliptic curves with complex multiplication, Lect. Notes Math.776, SpringerNew York (1980). Zbl0433.14032MR563921
12. [Im] Imai, H.: A remark on the rational points of abelian varieties with values in cyclotomic Zl-extensions, Proc. Jap. Acad.51 (1975), 12-16. Zbl0323.14010MR371902
13. [Ko] Kolyvagin, V.: Euler Systems, in The Grothendieck Festschrift, Volume II, P.I.M.87, BirkhäuserBoston1990. Zbl0742.14017MR1106906
14. [Mat] Matsumura, H.: Commutative Ring Theory, C.U.P.Cambridge1989. Zbl0666.13002MR1011461
15. [Mc1] McConnell, G.: On the Iwasawa theory of elliptic curves over cyclotomic fields, Ph.D. thesis, University of Cambridge1993. 
16. [Mc2] McConnell, G.: On a conjecture of Mazur for modular elliptic curves of analytic rank one, to appear. 
17. [McY] McConnell, G. and Yager, R.: Arithmetic of CM elliptic curves at supersingular primes, in preparation. 
18. [Mi] Milne, J.S.: Arithmetic Duality Theorems, Academic PressOrlando (1986). Zbl0613.14019MR881804
19. [P-R1] Perrin-Riou, B.: Arithmétique des courbes elliptiques et théorie d'lwasawa, thesis, Soc. Math. de France, Mémoire 17 (1984). 
20. [P-R2] Perrin-Riou, B.: Théorie d'lwasawa et hauteurs p-adiques: cas des variétés abéliennes, Séminaire de théorie des nombres de Paris90/91. Zbl0838.11072
21. [P-R3] Perrin-Riou, B.: Théorie d'Iwasawa et hauteurs p-adiques, Invent. Math.109 (1992), 137-185. Zbl0781.14013MR1168369
22. [Ro] Rohrlich, D.E.: On L-functions of elliptic curves and cyclotomic towers', Invent. Math.75, 409-423 (1984). Zbl0565.14006MR735333
23. [Ru1] Rubin, K.: Elliptic curves with complex multiplication and the Conjecture of Birch and Swinnerton-Dyer, Invent. Math.64 (1981), 455-470. Zbl0506.14039MR632985
24. [Ru2] Rubin, K.: Local units, elliptic units, Heegner points and elliptic curves, Invent. Math.88 (1987), 405-422. Zbl0623.14006MR880958
25. [Ru3] Rubin, K.: On the main conjecture of Iwasawa theory for imaginary quadratic fields, Invent. Math.93 (1988) 701-713. Zbl0673.12004MR952288
26. [Ru4] Rubin, K.The 'Main Conjectures' of Iwasawa theory for imaginary quadratic fields, Invent. Math.103 (1991), 25-68. Zbl0737.11030MR1079839
27. [Sc] Schneider, P.: p-adic height pairings II, Inv. Math.79, 329-374 (1985). Zbl0571.14021MR778132
28. [Se1] Serre, J.-P.: Algèbre Locale - Multiplicités, Springer-Verlag (2nd edition) 1965. Zbl0142.28603MR201468
29. [Se2] Serre, J.-P.Serre, Local Fields, Springer-Verlag, New York1979. Zbl0423.12016MR554237
30. [SeTa] Serre, J.-P. and Tate, J.: Good Reduction of Abelian Varieties, Ann. of Math.88 (1968), 492-517. Zbl0172.46101MR236190
31. [Si] Silverman, J.H.: The Arithmetic of Elliptic Curves, Springer-Verlag, New York1988. Zbl0585.14026MR817210
32. [Ta] Tate, J.: Relations between K2 and Galois Cohomology, Invent. Math.36, 257-274 (1976). Zbl0359.12011MR429837
33. [Wing] Wingberg, K.: Duality Theorems for Abelian Varieties over Zp-extensions, Advanced Studies in Pure Math.17, 471-492 (1989). Zbl0746.14011MR1097629
34. [Wint] Wintenberger, J.-P.: Structure Galoisienne de limites projectives d'unités locales, Compos. Math.421 (1981) 89-103. Zbl0414.12008MR594484