论文标题
朝着算术功能领域的猜想
Toward Fermat's conjecture over arithmetic function fields
论文作者
论文摘要
令k为一个算术函数字段，即有限类型的字段在理性数字字段上。在本说明中，作为由于陈 - 莫里瓦基（Chen-Moriwaki）的高度理论的应用，我们想表明，k n仅由0或几乎是正整数n组成的Fermat曲线曲线x^n + y^n = 1的解。更确切地说，该n的密度是1。
Let K be an arithmetic function field, that is, a field of finite type over the rational number field. In this note, as an application of the height theory due to Chen-Moriwaki, we would like to show that the solutions of Fermat's curve X^N + y^N = 1 of degree N over K consist of only either 0 or roots of unity for almost positive integers N. More precisely, the density of such N is 1.
