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Israel Journal of Mathematics

, Volume 85, Issue 1–3, pp 79–83 | Cite as

Curves with infinitely many points of fixed degree

  • Gerhard Frey
Article

Abstract

Thed-th symmetric productC (d) of a curveC defined over a fieldK is closely related to the set of points ofC of degree ≤d. IfK is a number field, then a conjecture of Lang [Hi] proved by Faltings [Fa2] implies ifC (d) (K) is an infinite set, then there is aK-rational covering ofC → ℙ |K 1 of degree ≤2d. As an application one gets that for fixed fieldK and fixedd there are only finitely many primes ι such that the set of all elliptic curves defined over some extensionsL ofK with [LK]≤d and withL-rational isogeny of degree ι is infinite.

Keywords

Elliptic Curf Abelian Variety Number Field Minimal Covering Symmetric Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1994

Authors and Affiliations

  1. 1.Institut für Experimentelle MathematikUniversität GH EssenEssen 12Germany

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