Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T11:41:39.474Z Has data issue: false hasContentIssue false
  • English
  • Français

Kummer theory on the product of an elliptic curve by the multiplicative group

Published online by Cambridge University Press:  18 May 2009

D. Bertrand
D. Bertrand
Affiliation:
Centre de Mathématioues de L'Ecole Polytechnique, 91128 Palaiseau Cedex, France
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This note extends classical results on certain Galois groups attached to onedimensional algebraic groups. We prove that the fields arising from the division of a fixed set of rational points on the product of an elliptic curve by the multiplicative group are as “large” as possible.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 1 , January 1981 , pp. 83 - 88
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

1.Baker, A. and Masser, D., Transcendence theory: advances and applications (Academic Press, 1977).Google Scholar
2.Bashmakov, M., The cohomology of abelian varieties over a number field, Russian Math. Surveys 27 (1972), 25–70.CrossRefGoogle Scholar
3.Bertrand, D., Sous-groupes à un paramètre p-adique de variétés de groupe, Invent. Math. 40 (1977), 171–193.CrossRefGoogle Scholar
4.Bertrand, D., Approximations diophantiennes p-adiques sur les courbes elliptiques admettant une multiplication complexe, Compositio Math. 37 (1978), 21–50.Google Scholar
5.Coates, J., An application of the division theory of elliptic curves to diophantine approximation, Invent. Math. 11, (1970), 167–182.CrossRefGoogle Scholar
6.Lang, S., Elliptic curves: diophantine analysis (Springer, 1978).CrossRefGoogle Scholar
7.Lang, S., Diophantine geometry (Wiley-Interscience, 1962).Google Scholar
8.Masser, D., Some results in transcendence theory, Journees arithmetiques de Luminy, 1978, Asterisque 61.Google Scholar
9.Ribet, K., Dividing rational points on abelian varieties of CM-type, Compositio Math. 33 (1976), 69–74.Google Scholar
10.Ribet, K., Kummer theory on extensions of abelian varieties by tori, Duke Math. J. 46 (1979), 745–761.CrossRefGoogle Scholar
11.Serre, J.-P., Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math. 15 (1972), 259–331.CrossRefGoogle Scholar