Around the Chevalley-Weil Theorem

TL;DR

This paper offers a new, topologically-based proof of the Chevalley-Weil Theorem with weaker assumptions, and applies it to simplify solutions of generalized Fermat equations.

Contribution

It provides an alternative proof of the Chevalley-Weil Theorem with relaxed hypotheses and demonstrates its application to generalized Fermat equations.

Findings

New topological proof of Chevalley-Weil Theorem

Simplification of arguments in generalized Fermat equations

Weaker hypotheses compared to traditional proofs

Abstract

We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an application to solutions of generalized Fermat equations, where our statement allows to simplify the original argument of Darmon and Granville.