Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shafarevich
Acta Arithmetica (2000)
- Volume: 93, Issue: 4, page 303-327
- ISSN: 0065-1036
Access Full Article
topHow to cite
topAbderrahmane Nitaj. "Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shafarevich." Acta Arithmetica 93.4 (2000): 303-327. <http://eudml.org/doc/207416>.
@article{AbderrahmaneNitaj2000,
author = {Abderrahmane Nitaj},
journal = {Acta Arithmetica},
keywords = {courbe de Frey-Hellegouarch; groupe de Tate-Shafarevich; conjecture de Goldfeld-Szpiro; Goldfeld-Szpiro conjecture},
language = {fre},
number = {4},
pages = {303-327},
title = {Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shafarevich},
url = {http://eudml.org/doc/207416},
volume = {93},
year = {2000},
}
TY - JOUR
AU - Abderrahmane Nitaj
TI - Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shafarevich
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 4
SP - 303
EP - 327
LA - fre
KW - courbe de Frey-Hellegouarch; groupe de Tate-Shafarevich; conjecture de Goldfeld-Szpiro; Goldfeld-Szpiro conjecture
UR - http://eudml.org/doc/207416
ER -
References
top- [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160.
- [2] C. Batut, D. Bernardi, H. Cohen and M. Olivier, PARI-GP, a computer system for number theory, Version 2.0, ftp://megrez.math.u-bordeaux.fr/pub/pari/.
- [3] R. Bölling, Die Ordnung der Schafarewitsch-Tate-Gruppe kann beliebig groß werden, Math. Nachr. 67 (1975), 157-179. Zbl0314.14008
- [4] J. W. S. Cassels, Arithmetic on curves of genus 1. VI. The Tate-Šafarevič group can be arbitrarily large, J. Reine Angew. Math. 214/215 (1964), 65-70. Zbl0236.14012
- [5] H. Cohen, A Course in Computational Algebraic Number Theory, Grad. Texts in Math. 138, Springer, Berlin, 1993.
- [6] I. Connell, APECS, Version 4.36 1998, ftp://math.mcgill.ca/pub/apecs/.
- [7] J. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, Cambridge, 1992. Zbl0758.14042
- [8] P. Deligne, Les constantes des équations fonctionnelles des fonctions L, in: Antwerp II: Modular Functions of One Variable, Lecture Notes in Math. 349, Springer, 1973, 501-597.
- [9] F. Diamond, On deformation rings and Hecke rings, Ann. of Math. 144 (1996), 137-166. Zbl0867.11032
- [10] F. Diamond and K. Kramer, Modularity of a family of elliptic curves, Math. Res. Lett. 2 (1995), 299-304. Zbl0867.11041
- [11] G. Frey, Some aspects of the theory of elliptic curves over number fields, Exposition. Math. 4 (1986), 35-66. Zbl0596.14022
- [12] J. Gebel and H. G. Zimmer, Computing the Mordell-Weil group of an elliptic curve over ℚ, in: Elliptic Curves and Related Topics, CRM Proc. Lecture Notes 4, Amer. Math. Soc., 1994, 61-83. Zbl0809.14024
- [13] D. Goldfeld and D. Lieman, Effective bounds on the size of the Tate-Shafarevich group, Math. Res. Lett. 3 (1996), 309-318. Zbl0869.11053
- [14] D. Goldfeld and L. Szpiro, Bounds for the order of the Tate-Shafarevich group, Compositio Math. 97 (1995), 71-87. Zbl0860.11032
- [15] B. H. Gross, Kolyvagin's work on modular elliptic curves, in: L-functions and Arithmetic (Durham, 1989), Cambridge Univ. Press, 1991, 235-256. Zbl0743.14021
- [16] D. Husemöller, Elliptic Curves, Grad. Texts in Math. 111, Springer, Berlin, 1986.
- [17] W. Kohnen and D. Zagier, Values of L-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), 175-198. Zbl0468.10015
- [18] V. A. Kolyvagin, Finiteness of E(ℚ) and Ш(E/ℚ) for a subclass of Weil curves, Math. USSR-Izv. 32 (1989), 523-541.
- [19] K. Kramer, A family of semistable elliptic curves with large Tate-Shafarevitch groups, Proc. Amer. Math. Soc. 89 (1983), 379-386. Zbl0567.14018
- [20] D. S. Kubert, Universal bounds on the torsion of elliptic curves, Proc. London Math. Soc. 33 (1976), 193-237. Zbl0331.14010
- [21] S. Lang, Conjectured diophantine estimates on elliptic curves, in: Progr. Math. 35, Birkhäuser, 1983, 155-172. Zbl0529.14017
- [22] A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534. Zbl0488.12001
- [23] L. Mai and M. R. Murty, A note on quadratic twists of an elliptic curve, in: Elliptic Curves and Related Topics, CRM Proc. Lecture Notes 4, Amer. Math. Soc., 1994, 121-124. Zbl0806.14025
- [24] Y. Manin, Cyclotomic fields and modular curves, Russian Math. Surveys 26 (1971), 7-78.
- [25] A. Nitaj, Détermination de courbes elliptiques pour la conjecture de Szpiro, Acta Arith. 85 (1998), 351-376. Zbl0914.11028
- [26] A. Nitaj, Tables of good abc-examples, preprint, Saarbrücken, 1997.
- [27] C. S. Rajan, On the size of the Shafarevich-Tate group of elliptic curves over function fields, Compositio Math. 105 (1997), 29-41. Zbl1044.11583
- [28] D. E. Rohrlich, Galois theory, elliptic curves, and root numbers, ibid. 100 (1996), 311-349. Zbl0860.11033
- [29] K. Rubin, Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987), 527-560. Zbl0628.14018
- [30] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106, Springer, Berlin, 1986.
- [31] Simath Group, SIMATH, a computer algebra system, Version 4.2, Saarbrücken, 1998, ftp://ftp.math.uni-sb.de:/pub/simath.
- [32] B. M. M. de Weger, A+B=C and big Ш's, Quart. J. Math. Oxford Ser. (2) 49 (1998), 105-128.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.