Fragments of the GL2 Iwasawa theory of elliptic curves without complex multiplication

  • John Coates
Part of the Lecture Notes in Mathematics book series (LNM, volume 1716)


Exact Sequence Elliptic Curf Galois Group Open Subgroup Finite Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. Balister, S. Howson, Note on Nakayama’s lemma for compact Λ-modules, Asian J. Math., 1 (1997), 214–219.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    K. Barré-Sirieix, G. Diaz, F. Gramain, G. Philibert, Une preuve de la conjecture de Mahler-Manin, Invent. Math.. 124 (1996), 1–9.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    J. Coates, G. McConnell, Iwasawa theory of modular elliptic curves of analytic rank at most 1, J. London Math. Soc., 50 (1994), 243–264.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Coates, R. Greenberg, Kummer theory for abelian varieties over local fields, Invent. Math., 124 (1996), 129–174.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    J. Coates, S. Howson, Euler characteristics and elliptic curves, Proc. Nat. Acad. Sci. USA, 94 (1997), 11115–11117.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    J. Coates, S. Howson, Euler characteristics and elliptic curves II, in preparation.Google Scholar
  7. [7]
    J. Coates, R. Sujatha, Galois cohomology of elliptic curves, Lecture Notes at the Tata Institute of Fundamental Research, Bombay (to appear).Google Scholar
  8. [8]
    J. Coates, R. Sujatha, Iwasawa theory of elliptic curves, to appear in Proc. Number Theory Conference held at KIAS, Seoul, December 1997.Google Scholar
  9. [9]
    J. Cremona, Algorithms for modular elliptic curves, 2nd edition, CUP (1997).Google Scholar
  10. [10]
    J. Dixon, M. du Sautoy, A. Mann, D. Segal, Analytic pro-p-groups, LMS Lecture Notes 157, CUP.Google Scholar
  11. [11]
    K. Goodearl, R. Warfield, An introduction to noncommutative Noetherian rings, LMS Student Texts 16, CUP.Google Scholar
  12. [12]
    R. Greenberg, Iwasawa theory for p-adic representations, Advanced Studies in Pure Math., 17 (1989), 97–137.MathSciNetzbMATHGoogle Scholar
  13. [13]
    R. Greenberg, Iwasawa theory for elliptic curves, this volume.Google Scholar
  14. [14]
    B. Gross, Kolyvagin’s work on modular elliptic curves, LMS Lecture Notes 153, CUP (1991), 235–256.zbMATHGoogle Scholar
  15. [15]
    Y. Hachimori, K. Matsuno, An analogue of Kida’s formula for the Selmer groups of elliptic curves, to appear in J. of Algebraic Geometry.Google Scholar
  16. [16]
    M. Harris, p-adic representations arising from descent on abelian varieties, Comp. Math. 39 (1979), 177–245.MathSciNetzbMATHGoogle Scholar
  17. [17]
    G. Hochschild, J.-P. Serre, Cohomology of group extensions, Trans. AMS, 74 (1953), 110–134.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    S. Howson, Iwasawa theory of elliptic curves for p-adic Lie extensions, Ph. D. thesis, Cambridge 1998.Google Scholar
  19. [19]
    K. Iwasawa, On ℤ -extensions of algebraic number fields, Ann. of Math., 98 (1973), 246–326.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    H. Imai, A remark on the rational points of abelian varieties with values in cyclotomic ℤ -extensions, Proc. Japan Acad., 51 (1975), 12–16.MathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    S. Lang, H. Trotter, Frobenius distributions in GL2-extensions, Springer Lecture Notes 504 (1976), Springer.Google Scholar
  22. [22]
    M. Lazard, Groupes analytiques p-adiques, Publ. Math. IHES, 26 (1965), 389–603.MathSciNetzbMATHGoogle Scholar
  23. [23]
    W. McCallum, Tate duality and wild ramification, Math. Ann., 288 (1990), 553–558.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Y. Ochi, Ph. D. thesis, Cambridge 1999.Google Scholar
  25. [25]
    J.-P. Serre, Cohomologie Galoisienne, Springer Lecture Notes 5, 5th edition (1994), Springer.Google Scholar
  26. [26]
    J.-P. Serre, Propriétés galoisiennes des points d’ordre fini des courbes elliptiques Invent. Math., 15 (1972), 259–331.MathSciNetCrossRefGoogle Scholar
  27. [27]
    J.-P. Serre, Abelian l-adic representations, 1968 Benjamin.Google Scholar
  28. [28]
    J.-P. Serre, Sur la dimension cohomologique des groupes profinis, Topology 3 (1965), 413–420.MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    J.-P. Serre, Sur les groupes de congruence des variétés abéliennes I, II, Izv. Akad. Nauk SSSR, 28 (1964), 3–20 and 35 (1971), 731–737.MathSciNetzbMATHGoogle Scholar
  30. [30]
    J.-P. Serre, La distribution d’Euler-Poincaré d’un groupe profini, to appear.Google Scholar
  31. [31]
    J.-P. Serre, J. Tate, Good reduction of abelian varieties, Ann. of Math. 88 (1968), 492–517.MathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    J. Silverman, The arithmetic of elliptic curves, Graduate Texts in Math. 106 (1986), Springer.Google Scholar
  33. [33]
    K. Wingberg, On Poincaré groups, J. London Math. Soc. 33 (1986), 271–278.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • John Coates
    • 1
  1. 1.Emmanuel CollegeCambridge

Personalised recommendations