Isogenies of prime degree over number fields

Fumiyuki Momose

Compositio Mathematica (1995)

  • Volume: 97, Issue: 3, page 329-348
  • ISSN: 0010-437X

How to cite

top

Momose, Fumiyuki. "Isogenies of prime degree over number fields." Compositio Mathematica 97.3 (1995): 329-348. <http://eudml.org/doc/90387>.

@article{Momose1995,
author = {Momose, Fumiyuki},
journal = {Compositio Mathematica},
language = {eng},
number = {3},
pages = {329-348},
publisher = {Kluwer Academic Publishers},
title = {Isogenies of prime degree over number fields},
url = {http://eudml.org/doc/90387},
volume = {97},
year = {1995},
}

TY - JOUR
AU - Momose, Fumiyuki
TI - Isogenies of prime degree over number fields
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 97
IS - 3
SP - 329
EP - 348
LA - eng
UR - http://eudml.org/doc/90387
ER -

References

top
  1. [Ab] Abramovich, D.: Formal finiteness and the uniform boundedness conjecture. A footnote to a paper of Kamienny and Mazur, preprint. Zbl0846.14013
  2. [C-S] Cornell, G. and Silverman, J.H.: Arithmetic Geometry. Springer-Verlag, Berlin (1985). Zbl0596.00007MR861969
  3. [D-R] Deligne, P. and Rapoport, M.: Schémas de modules des courbes elliptiques, Vol. II of the Proceedings of the International Summer School on Modular Functions, Antwerp (1972). Lecture Notes in Math. 349, Springer-Verlag, Berlin (1973). Zbl0281.14010MR337993
  4. [Fa] Falting, G. and Wüstholz et al.: Rational Points, Seminar Bonn/Wuppertal 1983-84, Aspects of Math., Friedr. Vieweg and Sohn (1984). Zbl0753.14019MR766573
  5. [Ka1] Kamienny, S.: Torsion points on elliptic curves and q-coefficients of modular forms, Invent. Math.109(2) (1992) 221-230. Zbl0773.14016MR1172689
  6. [Ka2] Kamienny, S.: A letter to B. Mazur. 
  7. [K-M] Kamienny, S. and Mazur B.: Rational torsion of prime order in elliptic curves over number fields, preprint. 
  8. [Ke1] Kenku, M.A.: On the modular curves X0(125), X 1(25) and X1(49), J. Lond. Math. Soc.23 (1981) 415-427. Zbl0425.14006MR616546
  9. [Ke2] Kenku, M.A.: Certain torsion points on elliptic curves defined over quadratic fields, J. Lond. Math. Soc.2 (1978) 233-240. Zbl0431.14007MR533321
  10. [K-Mo] Kenku, M.A. and Momose, F.: Torsion points on elliptic curves defined over quadratic fields, Nagoya Math. J.109 (1988) 125-149. Zbl0647.14020MR931956
  11. [La1] Lang, S.: Elliptic Functions, Addison-Wesley, Reading Math. (1973). Zbl0316.14001MR409362
  12. [La2] Lang, S.: Algebraic Number Theory, GTM110, Springer-Verlag (1970). MR1282723
  13. [Ma1] Mazur, B.: Modular curves and the Eisenstein ideal, Publ. Math. I.H.E.S. 47 (1977) 33-186. Zbl0394.14008MR488287
  14. [Ma2] Mazur, B.: Rational isogenies of prime degree, Invent. Math.44 (1978) 129-162. Zbl0386.14009MR482230
  15. [Mo] Momose, F.: p-Torsion points on elliptic curves defined over quadratic fields, Nagoya Math. J., 96 (1984) 139-165. Zbl0578.14021MR771075
  16. [O-T] Oort, F. and Tate, J.: Group schemes of prime order, Ann. Scient. Éc. Nórm. Sup., série 4, 3, 1-21 (1970). Zbl0195.50801MR265368
  17. [Ra1] Raynaud, M.: Schémas en groupes de type (p,...,p), Bull. Math. France102 (1974) 241-280. Zbl0325.14020MR419467
  18. [Ra2] Raynaud, M.: Spécialisation du fonctuer de Picard, Publ. Math. I.H.E.S. 38 (1970) 27-76. Zbl0207.51602
  19. [Ri] Ribet, K.A.: Endomorphisms of semistable abelian varieties over number fields, Ann. of Math.101 (1975) 552-562. Zbl0305.14016MR371903
  20. [Se] Serre, J.P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15 (1972) 259-331 Zbl0235.14012MR387283
  21. [S-T] Serre, J.P. and Tate, J.: Good reduction of abelian varieties, Ann. Math.88 (1968) 492-517. Zbl0172.46101MR236190
  22. [Mf] Modular functions of one variable IV, Lecture Notes in Math. 476, Springer-Verlag, Berlin (1975). 
  23. [SGA7] Groupes de Monodromie en Géométrie Algébrique (dirigé par A. Grothendieck avec collaboratiob de M. Raynaud et D. S. Rim), Lecture Notes in Math. 288, Springer-Verlag, Berlin (1972). Zbl0237.00013MR354656

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.