Torsion points on the modular jacobian J 0 ( N )

Dino J. Lorenzini

Compositio Mathematica (1995)

  • Volume: 96, Issue: 2, page 149-172
  • ISSN: 0010-437X

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Lorenzini, Dino J.. "Torsion points on the modular jacobian $J_0(N)$." Compositio Mathematica 96.2 (1995): 149-172. <http://eudml.org/doc/90360>.

@article{Lorenzini1995,
author = {Lorenzini, Dino J.},
journal = {Compositio Mathematica},
keywords = {Jacobian of modular curve; rational cuspidal points},
language = {eng},
number = {2},
pages = {149-172},
publisher = {Kluwer Academic Publishers},
title = {Torsion points on the modular jacobian $J_0(N)$},
url = {http://eudml.org/doc/90360},
volume = {96},
year = {1995},
}

TY - JOUR
AU - Lorenzini, Dino J.
TI - Torsion points on the modular jacobian $J_0(N)$
JO - Compositio Mathematica
PY - 1995
PB - Kluwer Academic Publishers
VL - 96
IS - 2
SP - 149
EP - 172
LA - eng
KW - Jacobian of modular curve; rational cuspidal points
UR - http://eudml.org/doc/90360
ER -

References

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  1. [BLR] S. Bosch, W. Lütkebohmert, and M. Raynaud, Néron Models, Springer Verlag, 1990. Zbl0705.14001MR1045822
  2. [Edi1] B. Edixhoven, Minimal resolution and stable reduction of X0(N), Ann. Inst. Fourier40, 1 (1990),31-67. Zbl0679.14009MR1056773
  3. [Edi2] B. Edixhoven, L' action de l'algèbre de Hecke sur le groupe des composantes des Jacobiennes des courbes modulaires est "Eisenstein", in Astérisque196-197 (1991), 159-170. Zbl0781.14019MR1141457
  4. [Kat] N. Katz, Galois properties of torsion points on abelian varieties, Inv. Math.62 (1981), 481-502. Zbl0471.14023MR604840
  5. [K-M] N. Katz and B. Mazur, Arithmetic moduli of elliptic curves, Princeton University Press, 1985. Zbl0576.14026MR772569
  6. [Lin] S. Ling, Congruences between cusps forms and the geometry of Jacobians of modular curves, Math. Ann.295 (1993), 111-133. Zbl0789.14027MR1198844
  7. [L-O] S. Ling and J. Oesterlé, The Shimura subgroup of J0(N), in Astérisque196-197 (1991), 171-203. Zbl0781.14015MR1141458
  8. [Lor1] D. Lorenzini, Arithmetical graphs, Math. Ann.285 (1989), 481-501. Zbl0662.14008MR1019714
  9. [Lor2] D. Lorenzini, Jacobians with potentially good l-reduction, J. Reine Angew. Math.430 (1992), 151-177. Zbl0821.14018MR1172912
  10. [Lor3] D. Lorenzini, The characteristic polynomial of a monodromy transformation attached to a family of curves, Comment. Math. Helvetici68 (1993), 111-137. Zbl0801.14006MR1201204
  11. [Lor4] D. Lorenzini, On the Jacobian of the modular curve X 0(N), Preprint (1993). 
  12. [Man] Y. Manin, Parabolic points and zeta functions of modular curves, Math. USSR Izvestija6 (1972), n° 1. Zbl0248.14010
  13. [Maz] B. Mazur, Modular curves and the Eisenstein ideal, Publ. I.H.E.S.47 (1977), 33-172. Zbl0394.14008MR488287
  14. [Ma-Ra] R. Mazur and M. Rapoport, Behavior of the Néron model of the Jacobian of X0(N) at bad primes, Publ. I.H.E.S.47 (1977), 173-185. 
  15. [Ogg1] A. Ogg, Rational points on certain elliptic modular curves, Proceedings of Symposia in Pure Mathematics 24, American Mathematical Society, 1973. Zbl0273.14008MR337974
  16. [Ogg2] A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France102 (1974), 449-462. Zbl0314.10018MR364259
  17. [Pou] D. Poulakis, La courbe modulaire X0(125) et sa jacobienne, J. Number Theory25 (1987), 112-131. Zbl0606.14029MR871172
  18. [Ray] M. Raynaud, Jacobienne des courbes modulaires et opérateurs de Hecke, in Astérisque196-197 (1991), 9-25. Zbl0781.14020MR1141454

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