The constant of the support problem for abelian varieties

JOURNAL OF NUMBER THEORY

卷:133

Article

Demeyer, Jeroen¹  Perucca, Antonella² 

[1] Univ Ghent, Dept Math, B-9000 Ghent, Belgium

[2] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

关键词: Abelian varieties;    Endomorphism;    Maximal order;    Support problem;    Tori;   

DOI  :  10.1016/j.jnt.2013.01.013

来源: Elsevier

【 摘 要 】

Let A be an abelian variety defined over a number field K and let P and Q be points in A(K) satisfying the following condition: for all but finitely many primes p of K. the order of (Q mod p) divides the order of (P mod p). Larsen proved that there exists a positive integer c such that cQ is in the End(K)(A)-module generated by P. We study the minimal value of c and construct some refined counterexamples. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free