Fermat's Last Theorem for Selmer sections

TL;DR

This paper proves that, within the framework of the section conjecture, all Selmer sections over the rational numbers for affine Fermat curves with exponent at least 7 are cuspidal, advancing understanding of the section conjecture.

Contribution

It establishes a new result confirming that Selmer sections are cuspidal for Fermat curves with exponent or rom 7 upwards, under the section conjecture.

Findings

All Selmer sections over or rom 7 are cuspidal.

Supports the section conjecture in the context of Fermat curves.

Provides new insights into the structure of Selmer sections.

Abstract

We prove, in the context of the section conjecture, that every Selmer section over $\mathbb{Q}$ of the affine Fermat curve with exponent $\ell$ is cuspidal for $\ell\geq 7$.