Jacobian Conjecture as a Problem on Integral Points on Affine Curves

被引：1
|
作者：
Van Nguyen, Chau [1 ]
机构：
[1] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam
来源：
VIETNAM JOURNAL OF MATHEMATICS | 2022年 / 50卷 / 01期
关键词：
Integral point; Polynomial map; Jacobian conjecture; POLYNOMIAL MAPS;
D O I：
10.1007/s10013-021-00488-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown that the Jacobian conjecture over number fields may be considered as an existence problem of integral points on affine curves. More specially, if the Jacobian conjecture over C is false, then for some n >> 1 there exists a counterexample F is an element of Z[X](n) of the form F-i(X) = X-i + (a(i1)X(1) + ... + a(in)X(n))(di), a(ij) is an element of Z, d(i) = 2; 3, i, j = 1, ... , n, such that the affine curve F-1(X) = F-2(X) = ... = F-n(X) has no non-zero integer points.
引用
收藏
页码：195 / 204
页数：10
相关论文
共 50 条
12345