no. 2
p-adic representations arising from descent on abelian varieties
Compositio Mathematica, Tome 39 (1979) no. 2, pp. 177-245 
@article{CM_1979__39_2_177_0,
     author = {Harris, Michael},
     title = {$p$-adic representations arising from descent on abelian varieties},
     journal = {Compositio Mathematica},
     pages = {177--245},
     year = {1979},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {39},
     number = {2},
     mrnumber = {546966},
     zbl = {0417.14034},
     language = {en},
     url = {https://www.numdam.org/item/CM_1979__39_2_177_0/}
}
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Harris, Michael. $p$-adic representations arising from descent on abelian varieties. Compositio Mathematica, Tome 39 (1979) no. 2, pp. 177-245. https://www.numdam.org/item/CM_1979__39_2_177_0/

[1] Modular Functions of One Variable IV, Lecture Notes in Mathematics, 476 (1975).

[2] E. Artin and J. Tate: Class Field Theory, New York: Benjamin (1967). | Zbl | MR

[3] M. Artin and B. Mazur: "Flat Arithmetic Duality," to appear.

[4] J. Ax: "On the Units of an Algebraic Number Field," Ill. J. Math., 9 (1965) 584-589. | Zbl | MR

[5] A. Brumer: "On the Units of Algebraic Number Fields," Mathematika, 14, 121-124, (1967). | Zbl | MR

[6] J.W.S. Cassels, "Diophantine Equations with Special Reference to Elliptic Curves," J. Lon. Math. Soc., 41, 193-291, (1966). | Zbl | MR

[7] J.W.S. Cassels: "The Rational Solutions of the Diophantine Equation Y2 = X3 - D," Acta Math., 82, 243-273, (1950). | Zbl | MR

[8] J. Coates: "On K2 and Some Classical Conjectures in Algebraic Number Theory," Ann. of Math., 95, 99-116, (1972). | Zbl | MR

[9] J. Coates and A. Wiles, "On the Conjecture of Birch and Swinnerton-Dyer," Inv. Math., 39, 223-251, (1977). | Zbl | MR

[10] P. Déligne: "Formes Modulaires et Représentations l-Adiques," Sem. Bourbaki 1968/69, Nº 355, Lecture Notes in Mathematics, 179 (1971). | Zbl | Numdam

[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). | Zbl | MR

[12] J. Dixmier: Algèbres Enveloppantes, Paris: Gauthier-Villars (1974). | Zbl | MR

[13] B. Ferrero: "Iwasawa Invariants of Abelian Number Fields," to appear. | Zbl | MR

[14] P. Gabriel: "Des Catégories Abeliens," Bull. Soc. Math. France, 90, 323-448, (1962). | Zbl | MR | Numdam

[ 15] A. Grothendieck: "Le Groupe de Brauer III: Exemples et Compléments," in Dix Exposés sur la Cohomologie des Schémas, Amsterdam: North-Holland, (1968). | Zbl | MR

[16] A. Grothendieck: "Modèles de Néron et Monodromie," in SGA 7, Lecture Notes in Mathematics, 288, (1972). | Zbl

[17] R. Greenberg: "The Iwasawa Invariants of Γ-Extensions of a Fixed Number Field," Am. J. Math., 95, 204-214, (1973). | Zbl

[18] R. Greenberg: "On p-Adic L--Functions and Cyclotomic Fields II," Nagoya Math. J., 67, 139-158 (1977). | Zbl | MR

[19] R. Greenberg: On the Iwasawa Invariants of Totally Real Number Fields," Am. J. Math., 98, 263-284, (1976). | Zbl | MR

[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] K. Iwasawa: "On Zl-Extensions of Algebraic Number Fields," Ann. of Math., 98, 246-326, (1973). | Zbl | MR

[22] K. Iwasawa: "A Note on Class Numbers of Algebraic Number Fields," Abh. Math. Sem. Univ. Hamburg, 20, 257-58, (1956). | Zbl | MR

[23] N. Katz: "P-Adic Interpolation of Real Analytic Eisenstein Series," Ann. of Math., 104, 459-571, (1976). | Zbl | MR

[24] M. Lazard: "Groupes Analytiques p-Adiques," Publ. Math. I.H.E.S., 26, (1965). | Zbl | MR | Numdam

[25] S. Lang: "Algebraic Groups over Finite Fields," Ann. J. Math., 78, 553-563, (1956). | Zbl | MR

[26] S. Lang: Elliptic Functions, Reading, Mass.: Addison-Wesley, (1973). | Zbl | MR

[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). | Zbl

[28] B. Mazur: "Rational Points of Abelian Varieties with Values in Towers of Number Fields," Inv. Math., 18, 183-266, (1972). | Zbl | MR

[29] B. Mazur: "Local Flat Duality," Am. J. Math., 92, 343-361, (1970). | Zbl | MR

[30] B. Mazur: "Rational Points of Modular Curves," in Modular Functions of One Variable V, Lecture Notes in Mathematics, 601, (1977). | Zbl | MR

[31] B. Mazur: "Trees of Rational Points of Elliptic Curves," unpublished manuscript.

[32] B. Mazur and L. Roberts: "Local Euler Characteristics," Inv. Math., 9, 201-234, (1970). | Zbl | MR

[33] B. Mazur and P. Swinnerton-Dyer: "Arithmetic of Weil Curves," Inv. Math., 25, 1-61, (1974). | Zbl | MR

[34] A. Néron: "Modèles Minimaux des Variétés Abéliennes sur les Corps Locaux et Globaux," Publ. Math. I.H.E.S., 21, (1964). | Zbl | MR | Numdam

[35] F. Oort and D. Mumford: "Deformations and Liftings of Finite, Commutative Group Schemes," Inv. Math., 5, 317-334, (1968). | Zbl | MR

[36] F. Oort and J. Tate: "Group Schemes of Prime Order," Ann. Sci. E.N.S., 3, 1-21, (1970). | Zbl | MR | Numdam

[37] M. Raynaud: "Schemas en Groupes de Type (p, ..., p)," Bull. Soc. Math. France, 102, 241-280, (1974). | Zbl | MR | Numdam

[38] L.G. Roberts: "The Flat Cohomology of Group Schemes of Rank p," Am. J. Math., 95, 688-702, (1973). | Zbl | MR

[39] J.-P. Serre: "Propriétés Galoisiennes des Points d'Ordre Fini des Courbes Elliptiques," Inv. Math., 15, 259-331, (1972). | Zbl | MR

[40] J.-P. Serre: "Classes de Corps Cyclotomiques," Sém. Bourbaki, Nº 174, (1958), New York: Benjamin (1966). | Zbl | Numdam

[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). | Zbl | MR

[42] J.-P. Serre: Abelian l-Adic Representations and Elliptic Curves, New York: Benjamin, (1968). | Zbl | MR

[43] J.-P. Serre: "Groupes Analytiques p-Adiques," Sém. Bourbaki, 1963/64, Nº 270, Secretariat Mathematiques, 11 Rue Pierre Curie, Paris 6e , (1964). | Zbl | MR | Numdam

[44] J.-P. Serre and J. Tate: "Good Reduction of Abelian Varieties," Ann. of Math., 88, 492-517, (1968). | Zbl | MR

[45] Séminaire de Geometrie Algebrique de Bois Marie, Lecture Notes in Mathematics, 269, 270, 305, (1972).

[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). | Zbl | MR

[47] J. Tate: "Algorithm for Determining the Type of a Singular Fiber in an Elliptic Pencil," in [1], 33-52. | MR

[48] J. Tate: "Global Class Field Theory," in Algebraic Number Theory, J.W.S. Cassels and A. Fröhlich, eds., New York: Academic Press, (1967). | MR

[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). | Zbl | MR

[50] M. Harris: "P-adic Representations of p-adic Groups," to appear in J. of Algebra. | MR

[51] M. Harris: "Systematic Growth of Mordell-Weil Groups of Abelian Varieties in Towers of Number Fields," to appear in Inv. Math. | Zbl | MR