Summary
A curve contained in a product of multiplicative groups passing through the origin, and containing infinitely many torsion points is a subgroup. The analogous statement on abelian varieties is discussed and reduced to an analogue of the irreducibility of the cyclotomic equation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Bibliography
J. Igusa,Fiber systems of elliptic curves, American Journal of Mathematics 81 (1959), pp. 453–476.
S. Lang,Diophantine Geometry, Intersience, 1962.
-- --,Integral points on curves, Publication l'I.H.E.S., No. 6 (1960) pp. 27–43.
J. Manin,Rational points of algebraic curves over function fields (in Russian), Izvestia Akademia Nauk 27 (1963), pp. 1395–1440.
J. P. Serre,Groupes de Lie l-adiques attachés aux courbes elliptiques, Colloque de Clermond-Ferrand (1964) pp. 197–212.
Author information
Authors and Affiliations
Additional information
In memory of Guido Castelnuovo in the recurrence of the first centenary of his birth.
Rights and permissions
About this article
Cite this article
Lang, S. Division points on curves. Annali di Matematica 70, 229–234 (1965). https://doi.org/10.1007/BF02410091
Issue Date:
DOI: https://doi.org/10.1007/BF02410091