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Fermat's Last Theorem for Selmer sections

Benjamin Steklov

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 $\ell\geq 7$.

Fermat's Last Theorem for Selmer sections

Abstract

We prove, in the context of the section conjecture, that every Selmer section over of the affine Fermat curve with exponent is cuspidal for .
Paper Structure (20 sections, 36 theorems, 140 equations)

This paper contains 20 sections, 36 theorems, 140 equations.

Table of Contents

  1. Introduction
  2. Method of proof
  3. The use of DM-stacks
  4. Outline of the paper
  5. DM-curves and their fundamental groups
  6. DM-curves
  7. Fundamental groups
  8. Inertia and decomposition groups
  9. The section conjecture for hyperbolic DM-curves
  10. The section conjecture for hyperbolic DM-curves
  11. Twists and centralizers
  12. Sub $p$-adic fields and Selmer sections
  13. The section conjecture for the moduli stack of elliptic curves
  14. The moduli stack of elliptic curves as a DM-curve
  15. Cuspidal sections and the Tate curve
  16. ...and 5 more sections

Key Result

Lemma 2.2

A one-dimensional algebraic space, which is smooth and separated over a field is a scheme.

Theorems & Definitions (79)

  • Definition 2.1
  • Lemma 2.2
  • Lemma 2.3
  • proof
  • proof
  • Theorem 2.5
  • proof
  • Proposition 2.6
  • proof
  • Lemma 2.7
  • ...and 69 more