Torsion points on families of products of elliptic curves

被引：26
作者：
Masser, D. [1 ]
Zannier, U. [2 ]
机构：
[1] Univ Basel, Math Inst, CH-4051 Basel, Switzerland
[2] Scuola Normale, I-56126 Pisa, Italy
来源：
ADVANCES IN MATHEMATICS | 2014年 / 259卷
关键词：
Torsion; Abelian scheme; Unlikely intersections; ANOMALOUS POINTS;
D O I：
10.1016/j.aim.2014.03.016
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In a recent paper we proved a special case of a variant of Pink's Conjecture for a variety inside a semiabelian scheme: namely for any curve inside any scheme isogenous to a fibred product of two isogenous elliptic schemes. Here we go ahead with the programme of settling the conjecture for general abelian surface schemes by completing the proof for all non-simple surfaces. This involves some entirely new and crucial issues. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：116 / 133
页数：18
相关论文
共 27 条
  • [1] ANDRE Y, 1992, COMPOS MATH, V82, P1
  • [2] [Anonymous], 1973, Elliptic Functions
  • [3] Bertrand D., 2013, ARXIV13071008V1, P40
  • [4] BERTRAND D, 1990, APPROXIMATIONS DIOPH, P39
  • [5] DIFFERENTIAL GALOIS THEORIES AND TRANSCENDANCE
    Bertrand, Daniel
    [J]. ANNALES DE L INSTITUT FOURIER, 2009, 59 (07) : 2773 - 2803
  • [6] Bombieri E, 2003, MICH MATH J, V51, P451
  • [7] On unlikely intersections of complex varieties with tori
    Bombieri, E.
    Masser, D.
    Zannier, U.
    [J]. ACTA ARITHMETICA, 2008, 133 (04) : 309 - 323
  • [8] DANILOV V. I., 1994, ALGEBRAIC GEOM, V23, P167
  • [9] Points of small height on elliptic curves
    David, S
    [J]. JOURNAL OF NUMBER THEORY, 1997, 64 (01) : 104 - 129
  • [10] Deligne P., 1971, PUBL MATH-PARIS, V40, P5, DOI 10.1007/BF02684692
123