References
[C] Casselman, W.: An Assortment of Results on Representations ofGL 2(k). In: Modular Functions of One Variable II, Lecture Notes in Mathematics, 349 (1973)
[De-Ra] Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. In: Modular Functions of One Variable II, Lecture Notes in Mathematics, 349 (1973)
[Dix] Dixmier, J.: Algèbres Enveloppantes, Paris: Gauthier-Villars, 1974
[H1] Harris, M.:P-adic Representations Arising from Descent on Abelian Varieties, Compositio Mathematica, in press (1979)
[H2] Harris, M.:P-adic Representations ofp-adic Groups, J. of Algebra, in press (1979)
[Iw] Iwasawa, K.: OnZ 1-Extensions of Algebraic Number Fields, Ann. of Math.,98, 246–326 (1973)
[J-L] Jacquet, H., Langlands, R.P.: Automorphic Forms onGL(2), Lecture Notes in Mathematics 114 (1970)
[K-L] Kubert, D., Lang, S.: Units in the Modular Function Field II, Math. Ann.218, 175–189 (1975)
[Ku1] Kurchanov, P.F.: Elliptic Curves of Infinite Rank over Γ-Extensions, Math. USSR Sbornik,19, 320–324 (1973)
[Ku2] Kurchanov, P.F.: Zeta-Functions of Elliptic Curves over Certain Abelian Extensions of Imaginary Quadratic Fields, (in Russian), Mat. Sbornik,102 (144) 56–70 (1977)
[L] Lazard, M.: Groupes Analytiquesp-adiques, Publ. Math. I.H.E.S., 26 (1965)
[M1] Mazur, B.: Rational Points of Abelian Varieties with Values in Towers of Number Fields, Inv. Math.,18, 183–266 (1972)
[M2] Mazur, B.: Trees of Rational Points on Elliptic Curves, unpublished manuscript
[M3] Mazur, B.: Rational Isogenies of Prime Degree, (with an appendix by D. Goldfeld), Inv. Math.,44, 129–162 (1978)
[M-Sw-D] Mazur, B., Swinnerton-Dyer, P.: Arithmetic of Weil Curves, Inv. Math.,25, 1–61 (1974)
[N] Nénron, A.: Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. I.H.E.S., 21 (1964)
[Ri1] Ribet, K.: Endomorphisms of Semi-Stable Abelian Varieties over Number Fields, Ann. of Math.,101, 555–562 (1975)
[Ri2] Ribet, K.: Galois Action on Division Points of Abelian Varieties with Real Multiplications, Am. J. Math.,98, 751–804 (1976)
[S1] Serre, J-P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Inv. Math.,15, 259–331 (1972)
[S2] Serre, J-P.: Abelianl-Adic Representations and Elliptic Curves, New York: Benjamin (1968)
[S3] Serre, J-P.: Arbres, Amalgames,SL 2, Astérisque, 46 (1977)
[Sh] Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions, Japan: Iwanomi Shoten, 1971
[Si] Silberger, A.J.:PGL 2 over thep-Adics: Its Representations, Spherical Functions, and Fourier Analysis, Lecture Notes in Mathematics 166 (1970)
[W] Weil, A.: Über die Bestimmung Dirichletscher Reihen durch Funktionalgeichungen, Math. Ann.,168, 149–156 (1967)
Author information
Authors and Affiliations
Additional information
Partially supported by an NSF Graduate Fellowship
Rights and permissions
About this article
Cite this article
Harris, M. Systematic growth of Mordell-Weil groups of abelian varieties in towers of number fields. Invent Math 51, 123–141 (1979). https://doi.org/10.1007/BF01390224
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01390224