$p$-adic representations arising from descent on abelian varieties

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1. [1] Modular Functions of One Variable IV, Lecture Notes in Mathematics, 476 (1975). 
2. [2] E. Artin and J. Tate: Class Field Theory, New York: Benjamin (1967). Zbl0176.33504MR223335
3. [3] M. Artin and B. Mazur: "Flat Arithmetic Duality," to appear. 
4. [4] J. Ax: "On the Units of an Algebraic Number Field," Ill. J. Math., 9 (1965) 584-589. Zbl0132.28303MR181630
5. [5] A. Brumer: "On the Units of Algebraic Number Fields," Mathematika, 14, 121-124, (1967). Zbl0171.01105MR220694
6. [6] J.W.S. Cassels, "Diophantine Equations with Special Reference to Elliptic Curves," J. Lon. Math. Soc., 41, 193-291, (1966). Zbl0138.27002MR199150
7. [7] J.W.S. Cassels: "The Rational Solutions of the Diophantine Equation Y2 = X3 - D," Acta Math., 82, 243-273, (1950). Zbl0037.02701MR35782
8. [8] J. Coates: "On K2 and Some Classical Conjectures in Algebraic Number Theory," Ann. of Math., 95, 99-116, (1972). Zbl0245.12005MR360523
9. [9] J. Coates and A. Wiles, "On the Conjecture of Birch and Swinnerton-Dyer," Inv. Math., 39, 223-251, (1977). Zbl0359.14009MR463176
10. [10] P. Déligne: "Formes Modulaires et Représentations l-Adiques," Sem. Bourbaki1968/69, Nº 355, Lecture Notes in Mathematics, 179 (1971). Zbl0206.49901
11. [11] P. Déligne and M. Rapoport: "Les Schémas de Modules de Courbes Elliptiques," in Modular Functions of One Variable II, Lecture Notes in Mathematics, 349, (1973). Zbl0281.14010MR337993
12. [12] J. Dixmier: Algèbres Enveloppantes, Paris: Gauthier-Villars (1974). Zbl0308.17007MR498737
13. [13] B. Ferrero: "Iwasawa Invariants of Abelian Number Fields," to appear. Zbl0347.12004MR485777
14. [14] P. Gabriel: "Des Catégories Abeliens," Bull. Soc. Math. France, 90, 323-448, (1962). Zbl0201.35602MR232821
15. [ 15] A. Grothendieck: "Le Groupe de Brauer III: Exemples et Compléments," in Dix Exposés sur la Cohomologie des Schémas, Amsterdam: North-Holland, (1968). Zbl0198.25901MR244271
16. [16] A. Grothendieck: "Modèles de Néron et Monodromie," in SGA 7, Lecture Notes in Mathematics, 288, (1972). Zbl0248.14006
17. [17] R. Greenberg: "The Iwasawa Invariants of Γ-Extensions of a Fixed Number Field," Am. J. Math., 95, 204-214, (1973). Zbl0268.12005
18. [18] R. Greenberg: "On p-Adic L--Functions and Cyclotomic Fields II," Nagoya Math. J., 67, 139-158 (1977). Zbl0373.12007MR444614
19. [19] R. Greenberg: On the Iwasawa Invariants of Totally Real Number Fields," Am. J. Math., 98, 263-284, (1976). Zbl0334.12013MR401702
20. [20] M. Hazewinkel: "On Norm Maps for One Dimensional Formal Groups I: The Cyclotomic Γ-Extension" Netherlands School of Economics, Econometric Institute, Report 7206, (1972). 
21. [21] K. Iwasawa: "On Zl-Extensions of Algebraic Number Fields," Ann. of Math., 98, 246-326, (1973). Zbl0285.12008MR349627
22. [22] K. Iwasawa: "A Note on Class Numbers of Algebraic Number Fields," Abh. Math. Sem. Univ. Hamburg, 20, 257-58, (1956). Zbl0074.03002MR83013
23. [23] N. Katz: "P-Adic Interpolation of Real Analytic Eisenstein Series," Ann. of Math., 104, 459-571, (1976). Zbl0354.14007MR506271
24. [24] M. Lazard: "Groupes Analytiques p-Adiques," Publ. Math. I.H.E.S., 26, (1965). Zbl0139.02302MR209286
25. [25] S. Lang: "Algebraic Groups over Finite Fields," Ann. J. Math., 78, 553-563, (1956). Zbl0073.37901MR86367
26. [26] S. Lang: Elliptic Functions, Reading, Mass.: Addison-Wesley, (1973). Zbl0316.14001MR409362
27. [27] Ju. I. Manin and M.M. Vishik: "P-Adic Hecke Series of Imaginary Quadratic Fields," (Trans.) Math. U.S.S.R. Sbornik, 24, 345-371, (1974). Zbl0329.12016
28. [28] B. Mazur: "Rational Points of Abelian Varieties with Values in Towers of Number Fields," Inv. Math., 18, 183-266, (1972). Zbl0245.14015MR444670
29. [29] B. Mazur: "Local Flat Duality," Am. J. Math., 92, 343-361, (1970). Zbl0199.24501MR271119
30. [30] B. Mazur: "Rational Points of Modular Curves," in Modular Functions of One Variable V, Lecture Notes in Mathematics, 601, (1977). Zbl0357.14005MR450283
31. [31] B. Mazur: "Trees of Rational Points of Elliptic Curves," unpublished manuscript. 
32. [32] B. Mazur and L. Roberts: "Local Euler Characteristics," Inv. Math., 9, 201-234, (1970). Zbl0191.19202MR258844
33. [33] B. Mazur and P. Swinnerton-Dyer: "Arithmetic of Weil Curves," Inv. Math., 25, 1-61, (1974). Zbl0281.14016MR354674
34. [34] A. Néron: "Modèles Minimaux des Variétés Abéliennes sur les Corps Locaux et Globaux," Publ. Math. I.H.E.S., 21, (1964). Zbl0132.41403MR179172
35. [35] F. Oort and D. Mumford: "Deformations and Liftings of Finite, Commutative Group Schemes," Inv. Math., 5, 317-334, (1968). Zbl0179.49901MR228505
36. [36] F. Oort and J. Tate: "Group Schemes of Prime Order," Ann. Sci. E.N.S., 3, 1-21, (1970). Zbl0195.50801MR265368
37. [37] M. Raynaud: "Schemas en Groupes de Type (p, ..., p)," Bull. Soc. Math. France, 102, 241-280, (1974). Zbl0325.14020MR419467
38. [38] L.G. Roberts: "The Flat Cohomology of Group Schemes of Rank p," Am. J. Math., 95, 688-702, (1973). Zbl0281.14020MR337972
39. [39] J.-P. Serre: "Propriétés Galoisiennes des Points d'Ordre Fini des Courbes Elliptiques," Inv. Math., 15, 259-331, (1972). Zbl0235.14012MR387283
40. [40] J.-P. Serre: "Classes de Corps Cyclotomiques," Sém. Bourbaki, Nº 174, (1958), New York: Benjamin (1966). Zbl0119.27603
41. [41] J.-P. Serre: "Sur les Groupes de Congruence des Variétés Abéliennes II," Izv. Akad. Nauk S.S.S.R., Ser. Mat., Tom 35, 731-737, (1971). Zbl0222.14025MR289513
42. [42] J.-P. Serre: Abelian l-Adic Representations and Elliptic Curves, New York: Benjamin, (1968). Zbl0186.25701MR263823
43. [43] J.-P. Serre: "Groupes Analytiques p-Adiques," Sém. Bourbaki, 1963/64, Nº 270, Secretariat Mathematiques, 11 Rue Pierre Curie, Paris 6e , (1964). Zbl0163.02901MR176987
44. [44] J.-P. Serre and J. Tate: "Good Reduction of Abelian Varieties," Ann. of Math., 88, 492-517, (1968). Zbl0172.46101MR236190
45. [45] Séminaire de Geometrie Algebrique de Bois Marie, Lecture Notes in Mathematics, 269, 270, 305, (1972). 
46. [46] J. Tate: "Duality Theorems in Galois Cohomology over Number Fields," Proc. Int. Cong. Math. Stockholm, 1962, 288-295. Institute Mittag-Leffler, Djursholm, Sweden, (1963). Zbl0126.07002MR175892
47. [47] J. Tate: "Algorithm for Determining the Type of a Singular Fiber in an Elliptic Pencil," in [1], 33-52. Zbl1214.14020MR393039
48. [48] J. Tate: "Global Class Field Theory," in Algebraic Number Theory, J.W.S. Cassels and A. Fröhlich, eds., New York: Academic Press, (1967). Zbl1179.11041MR220697
49. [49] M.M. Vishik: "The p-adic Zeta-Function of an Imaginary Quadratic Field and the Leopoldt Regulator," (Russian), Mat. Sbornik, 102 (144), 173-181, (1977). Zbl0443.12007MR480435
50. [50] M. Harris: "P-adic Representations of p-adic Groups," to appear in J. of Algebra. Zbl0497.22022MR1279255
51. [51] M. Harris: "Systematic Growth of Mordell-Weil Groups of Abelian Varieties in Towers of Number Fields," to appear in Inv. Math. Zbl0429.14013MR528019

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