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arXiv · 2001.11178

Toward Fermat's conjecture over arithmetic function fields

Atsushi Moriwaki
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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.

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Atsushi Moriwaki. 2020-01-30. Toward Fermat's conjecture over arithmetic function fields. https://arxiv.org/abs/2001.11178

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