Structures galoisiennes et courbes elliptiques

Philippe Cassou-Nogues; Martin J. Taylor

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 1, page 307-331
  • ISSN: 1246-7405

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Cassou-Nogues, Philippe, and Taylor, Martin J.. "Structures galoisiennes et courbes elliptiques." Journal de théorie des nombres de Bordeaux 7.1 (1995): 307-331. <http://eudml.org/doc/247652>.

@article{Cassou1995,
author = {Cassou-Nogues, Philippe, Taylor, Martin J.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Galois structure; elliptic curves; Hopf orders; principal homogeneous space; explicit determination of generators; group schemes; -adic -function of an elliptic curve; elliptic units; Picard invariant},
language = {fre},
number = {1},
pages = {307-331},
publisher = {Université Bordeaux I},
title = {Structures galoisiennes et courbes elliptiques},
url = {http://eudml.org/doc/247652},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Cassou-Nogues, Philippe
AU - Taylor, Martin J.
TI - Structures galoisiennes et courbes elliptiques
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 1
SP - 307
EP - 331
LA - fre
KW - Galois structure; elliptic curves; Hopf orders; principal homogeneous space; explicit determination of generators; group schemes; -adic -function of an elliptic curve; elliptic units; Picard invariant
UR - http://eudml.org/doc/247652
ER -

References

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  1. [A-T] S.A. Agboola et M.J. Taylor, Class invariants of Mordell- Weil groups, à paraître. Zbl0799.11049
  2. [B-T] S.N. Byott et M.J. Taylor, Hopf structure and Galois modules, Group rings and class groups, DMV seminar 18 (1992), Birkhaüser. Zbl0811.11068MR1167451
  3. [CN-S] Ph. Cassou-Noguès et A. Srivastav, Galois module structure of Kummer 2-extensions and elliptic curves of rank ≽ 1, à paraître. 
  4. [CN-T] Ph. Cassou-Noguès et M.J. Taylor, Espaces homogènes principaux, unités elliptiques et fonctions L, Ann. Inst.44 (1994), 631-661. Zbl0810.11039MR1303880
  5. [F1] A. Fröhlich, Invariants for modules over commutative separable orders, Quart J. Math. Oxford216 (1965), 193-232. Zbl0192.14002MR210697
  6. [F2] A. Frôhlich, Artin root numbers and normal integral bases for quaternion fields, Invent. Math.17 (1972), 143-166. Zbl0261.12008MR323759
  7. [Le] H.W. Leopoldt, Uber die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. reine angew Math.201 (1959), 119-149. Zbl0098.03403MR108479
  8. [F2] S. Lang, Cyclotomic fields, Graduate texts in Mathematics59, Springer-Verlag. Zbl0395.12005MR485768
  9. [M] J. Milne, Etale cohomology, Princeton Univ. Press, New Jersey (1980). Zbl0433.14012MR559531
  10. [PR] B. Perrin-Riou, Arithmétique des courbes elliptiques et théorie d'Iwasawa, Mémoire de la S.M.F.17 (1984). Zbl0599.14020
  11. [R] K. Rubin, p-adic L-functions and rational points on elliptic curves with complex multiplication, Invent. Math.107 (1992), 323-350. Zbl0770.11033MR1144427
  12. [Se-T] J.P. Serre et J. Tate, Good reduction of abelian varieties, Ann. of Math.68 (1968),492-517. Zbl0172.46101MR236190
  13. [S-T] A. Srivastav et M.J. Taylor, Elliptic curves with complex multiplication and Galois module structure, Invent. Math.99 (1990), 165-184. Zbl0705.14031MR1029394
  14. [SW] M.E. Sweedler, Hopf algebras, W.A. Benjamin, New York (1969). Zbl0194.32901MR252485
  15. [T1] M.J. Taylor, On Fröhlich's conjecture for rings of integers of tame extensions, Invent. Math.63 (1981), 41-79. Zbl0469.12003MR608528
  16. [T2] M.J. Taylor, Galois module structure of rings of integers in Kummer extensions, Bull. L.M.S.12 (1980), 96-98. Zbl0408.12017MR571727
  17. [W] W.C. Waterhouse, Principal homogeneous spaces and Group scheme extensions, Trans. A.M.S. 153 (1971), 181-189. Zbl0208.48401MR269659

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