Groupe de Selmer d'une courbe elliptique à multiplication complexe

Bernadette Perrin-Riou

Compositio Mathematica (1981)

  • Volume: 43, Issue: 3, page 387-417
  • ISSN: 0010-437X

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Perrin-Riou, Bernadette. "Groupe de Selmer d'une courbe elliptique à multiplication complexe." Compositio Mathematica 43.3 (1981): 387-417. <http://eudml.org/doc/89508>.

@article{Perrin1981,
author = {Perrin-Riou, Bernadette},
journal = {Compositio Mathematica},
keywords = {elliptic curve with complex multiplication; -extension; imaginary quadratic number field; Leopoldt conjecture; Selmer group; Mordell-Weil group; Birch-Swinnerton-Dyer conjecture},
language = {fre},
number = {3},
pages = {387-417},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {Groupe de Selmer d'une courbe elliptique à multiplication complexe},
url = {http://eudml.org/doc/89508},
volume = {43},
year = {1981},
}

TY - JOUR
AU - Perrin-Riou, Bernadette
TI - Groupe de Selmer d'une courbe elliptique à multiplication complexe
JO - Compositio Mathematica
PY - 1981
PB - Sijthoff et Noordhoff International Publishers
VL - 43
IS - 3
SP - 387
EP - 417
LA - fre
KW - elliptic curve with complex multiplication; -extension; imaginary quadratic number field; Leopoldt conjecture; Selmer group; Mordell-Weil group; Birch-Swinnerton-Dyer conjecture
UR - http://eudml.org/doc/89508
ER -

References

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  1. [1] D. Bernardi: Hauteurs p-adiques sur les courbes elliptiques. Séminaire Delange-Pisot-Poitou (1980). MR633886
  2. [2] B.J. Birch et H.P.F. Swinnerton-Dyer: Notes on elliptic curves I. J. reine angew. Math., 212 (1963) 7-25. Zbl0118.27601MR146143
  3. [3] J.W.S. Cassels: Arithmetic on curves of genus 1. J. reine angew. Math. (IV) 207 (1962) 234-246, (VIII) 217 (1965) 180-189. Zbl0241.14017MR179169
  4. [4] J.- Coates: Kummer's criterium for Hurwitz numbers. Proceedings of the International Congress on Algebraic Number Theory, Japan: Kyoto (1976). 
  5. [5] J. Coates: Elliptic curves with complex multiplication. Hermann Weyl lectures1979, Annals of Math. Studies (à paraitre). 
  6. [6] R. Greenberg: On the structure of certains Galois groups. Inventiones Math.47 (1978) 85-99. Zbl0403.12004MR504453
  7. [7] B.H. Gross: Arithmetic on elliptic curves with complex multiplication. Lecture notes in Mathematics776, Berlin-Heidelberg-New York: Springer (1980). Zbl0433.14032MR563921
  8. [8] M. Harris: P-adic representation arising from descent on abelian varieties. Compositio Mathematica, 39 (1979) 177-245. Zbl0417.14034MR546966
  9. [9] M. Harris: Systematic growth of Mordell-Weil groups of abelian varieties in towers of number fields. Inventiones Math.51 (1979) 123-141. Zbl0429.14013MR528019
  10. [10] P.F. Kurchanov: Elliptic curves of infinite rank over Γ-extensions. Mat. U.S.S.R. Sbornik. Vol 19, No. 2 (1973). Zbl0273.14009
  11. [11] S. Lang et J. Tate: Principal homogeneous spaces over abelian varieties. American J. of Math.78 (1956) 659-684. Zbl0097.36203MR106226
  12. [12] B. Mazur: Rational points on abelian varieties with values in towers of number fields. Inventiones Math.18 (1972) 183-266. Zbl0245.14015MR444670
  13. [13] B. Mazur: Trees of rational points on elliptic curves. (Non publié). 
  14. [14] J.-P. Wintenberger: Structure galoisienne de limites projectives d'unités locales. Compositio Mathematica, 42 (1980) 89-104. Zbl0414.12008MR594484

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