Year: 2020
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Moriwaki, Atsushi
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3003477366