Comptes Rendus
Théorie des nombres/Géométrie algébrique
Points algébriques sur certains quotients de courbes de Fermat
[Algebraic points on some quotients of Fermat curves]
Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 117-120.

We determine explicitly algebraic points of a given degree on some quotients of Fermat curves of degree 5, 7 or 11. This Note completes previous work of Gross and Rohrlich (Invent. Math. 44 (1978) 201–224) who gave a description of points of degree at most two.

Nous déterminons explicitement les points algébriques de degré donné quelconque sur certains quotients de courbes de Fermat de degré 5, 7 ou 11. Cette Note complète les travaux de Gross et Rohrlich (Invent. Math. 44 (1978) 201–224) qui donnent la description de l'ensemble des points algébriques de degré au plus 2 sur les courbes étudiées.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)00028-6

Oumar Sall 1

1 U.F.R. de mathématiques, Université Paris 7-Denis Diderot, 175, rue de Chevaleret, 75013 Paris, France
@article{CRMATH_2003__336_2_117_0,
     author = {Oumar Sall},
     title = {Points alg\'ebriques sur certains quotients de courbes de {Fermat}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {117--120},
     publisher = {Elsevier},
     volume = {336},
     number = {2},
     year = {2003},
     doi = {10.1016/S1631-073X(02)00028-6},
     language = {fr},
}
TY  - JOUR
AU  - Oumar Sall
TI  - Points algébriques sur certains quotients de courbes de Fermat
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 117
EP  - 120
VL  - 336
IS  - 2
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)00028-6
LA  - fr
ID  - CRMATH_2003__336_2_117_0
ER  - 
%0 Journal Article
%A Oumar Sall
%T Points algébriques sur certains quotients de courbes de Fermat
%J Comptes Rendus. Mathématique
%D 2003
%P 117-120
%V 336
%N 2
%I Elsevier
%R 10.1016/S1631-073X(02)00028-6
%G fr
%F CRMATH_2003__336_2_117_0
Oumar Sall. Points algébriques sur certains quotients de courbes de Fermat. Comptes Rendus. Mathématique, Volume 336 (2003) no. 2, pp. 117-120. doi : 10.1016/S1631-073X(02)00028-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)00028-6/

[1] D. Abramovic; J. Harris Abelian varieties and curves in Wd(C), Compositio Math., Volume 78 (1991), pp. 227-238

[2] O. Debarre; R. Fahlaoui Abelian varieties and curves in Wdr(C) and points of bounded degree on algebraic curves, Compositio Math., Volume 88 (1993), pp. 235-249

[3] O. Debarre; M. Klassen Points of low degree on smooth plane curves, J. Reine Angew. Math., Volume 446 (1994), pp. 81-87

[4] Diophantine approximation on Abelian varieties, Ann. Math. 133 (1991) 549–576

[5] D. Faddeev On the divisor class groups of some algebraic curves, English translation: Soviet Math. Dokl., Volume 136 (1961) no. 1, pp. 296-298

[6] G. Faltings Endlichkeitsätze für abelsch Varietäten über Zahlkörpen, Invent. Math., Volume 73 (1983), pp. 349-366

[7] G. Frey Curves with infinitely many points of fixed degree, Israel J. Math., Volume 85 (1994), pp. 79-83

[8] B. Gross; D. Rohrlich Some results on the Mordell–Weil group of the Jacobian of the Fermat curve, Invent. Math., Volume 44 (1978), pp. 201-224

[9] M. Klassen; P. Tzermias Algebraic points of low degree on the Fermat quintic, Acta Arith., Volume 82 (1997) no. 4, pp. 393-401

[10] O. Sall Points algébriques de petit degré sur les courbes de Fermat, C. R. Acad. Sci. Paris Sér. I, Volume 330 (2000), pp. 67-70

[11] O. Sall Points cubiques sur la quartique de Klein, C. R. Acad. Sci. Paris Sér. I, Volume 333 (2001), pp. 931-934

[12] P. Tzermias Algebraic points of low degree on the Fermat curve of degree seven, Manuscriptc Math., Volume 97 (1998) no. 4, pp. 483-488

[13] P. Tzermias Torsion parts of Mordell–Weil groups of Fermat Jacobians, Internat. Math. Res. Notices, Volume 7 (1998), pp. 359-369

[14] Siegel's theorem in the compact case, Ann. Math. 133 (1991) 509–548

Cited by Sources:

Comments - Policy