Toward Fermat's conjecture over arithmetic function fields
Number Theory
2020-01-31 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2001.11178,
title = {Toward Fermat's conjecture over arithmetic function fields},
author = {Atsushi Moriwaki},
journal= {arXiv preprint arXiv:2001.11178},
year = {2020}
}
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7 pages