Elliptic Curves over the Perfect Closure of a Function Field
Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 87-94

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that the group of rational points of a non-isotrivial elliptic curve defined over the perfect closure of a function field in positive characteristic is finitely generated.
DOI : 10.4153/CMB-2010-019-9
Mots-clés : 11G50, 11G05, elliptic curves, heights
Ghioca, Dragos. Elliptic Curves over the Perfect Closure of a Function Field. Canadian mathematical bulletin, Tome 53 (2010) no. 1, pp. 87-94. doi: 10.4153/CMB-2010-019-9
@article{10_4153_CMB_2010_019_9,
     author = {Ghioca, Dragos},
     title = {Elliptic {Curves} over the {Perfect} {Closure} of a {Function} {Field}},
     journal = {Canadian mathematical bulletin},
     pages = {87--94},
     year = {2010},
     volume = {53},
     number = {1},
     doi = {10.4153/CMB-2010-019-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-019-9/}
}
TY  - JOUR
AU  - Ghioca, Dragos
TI  - Elliptic Curves over the Perfect Closure of a Function Field
JO  - Canadian mathematical bulletin
PY  - 2010
SP  - 87
EP  - 94
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-019-9/
DO  - 10.4153/CMB-2010-019-9
ID  - 10_4153_CMB_2010_019_9
ER  - 
%0 Journal Article
%A Ghioca, Dragos
%T Elliptic Curves over the Perfect Closure of a Function Field
%J Canadian mathematical bulletin
%D 2010
%P 87-94
%V 53
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-019-9/
%R 10.4153/CMB-2010-019-9
%F 10_4153_CMB_2010_019_9

[1] [1] Baker, M. H. and Silverman, J. H., A lower bound for the canonical height on abelian varieties over abelian extensions. Math. Res. Lett. 11(2004), no. 2–3, 377–396. Google Scholar

[2] [2] David, S. and Hindry, M., Minoration de la hauteur de Néron-Tate sur les variétés abéliennes de type C. M. J. Reine Angew. Math. 529(2000), 1–74. Google Scholar

[3] [3] Dobrowolski, E., On a question of Lehmer and the number of irreducible factors of a polynomial. Acta Arith. 34(1979), no. 4, 391–401. Google Scholar

[4] [4] Ghioca, D. and Moosa, R., Division points of subvarieties of isotrivial semi-abelian varieties. Int. Math. Res. Not. 2006, Art. ID 65437. Google Scholar

[5] [5] Goldfeld, D. and Szpiro, L., Bounds for the order of the Tate-Shafarevich group. Compositio Math. 97(1995), no. 1–2, 71–87 Google Scholar

[6] [6] Hindry, M. and Silverman, J. H., The canonical height and integral points on elliptic curves. Invent. Math. 93(1988), no. 2, 419–450. doi:10.1007/BF01394340 Google Scholar

[7] [7] Hindry, M. and Silverman, J. H., On Lehmer's conjecture for elliptic curves. In: Séminaire de Théorie des Nombres, Paris 1988-1989, Progr. Math. 91, Birkhäuser Boston, Boston, MA, 1990, pp. 103–116. Google Scholar

[8] [8] Kim, M., Purely inseparable points on curves of higher genus. Math. Res. Lett. 4(1997), no. 5, 663–666. Google Scholar

[9] [9] Lang, S., Fundamentals of Diophantine geometry. Springer-Verlag, New York, 1983. Google Scholar

[10] [10] Lang, S., Number theory. III. Diophantine geometry. In: Encyclopaedia of Mathematical Sciences 60, Springer-Verlag, Berlin, 1991. Google Scholar

[11] [11] Laurent, M., Minoration de la hauteur de Néron-Tate. In: Séminaire de théorie des nombres, Paris 1981–82, Progr. Math. 38, Birkhäuser Boston, Boston, MA, 1983, pp. 137–151. Google Scholar

[12] [12] Lehmer, D. H., Factorization of certain cyclotomic functions. Ann. of Math. (2) 34(1933), no. 3, 461–479. doi:10.2307/1968172 Google Scholar

[13] [13] Levin, M., On the group of rational points on elliptic curves over function fields. Amer. J. Math. 90(1968), 456–462. doi:10.2307/2373538 Google Scholar

[14] [14] Masser, D. W., Counting points of small height on elliptic curves. Bull. Soc. Math. France 117(1989), no. 2, 247–265. Google Scholar

[15] [15] Poonen, B., Local height functions and the Mordell-Weil theorem for Drinfeld modules. Compositio Math. 97(1995), no. 3, 349–368. Google Scholar

[16] [16] Scanlon, T., A positive characteristic Manin-Mumford theorem. Compositio Math. 141(2005), no. 6, 1351–1364. doi:10.1112/S0010437X05001879 Google Scholar

[17] [17] Serre, J.-P., Lectures on the Mordell-Weil theorem. Aspects of Mathematics E15, Friedr. Vieweg & Sohn, Braunschweig, 1989. Google Scholar

[18] [18] Silverman, J. H., The arithmetic of elliptic curves. Graduate Texts in Mathematics 106, Springer-Verlag, New York, 1986. Google Scholar

[19] [19] Silverman, J. H., Advanced topics in the arithmetic of elliptic curves. Graduate Texts in Mathematics 151, Springer-Verlag, New York, 1994. Google Scholar

[20] [20] Silverman, J. H., A lower bound for the canonical height on elliptic curves over abelian extensions. J. Number Theory 104(2004), no. 2, 353–372. doi:10.1016/j.jnt.2003.07.001 Google Scholar

Cité par Sources :