Quantitative Chevalley-Weil theorem for curves

TL;DR

This paper provides an explicit quantitative version of the Chevalley-Weil theorem for algebraic curves, bounding the discriminant of fields of definition for fibers over rational points.

Contribution

It offers a fully explicit, dimension-one version of the classical Chevalley-Weil theorem, enhancing its applicability with concrete bounds.

Findings

Explicit bounds on discriminants for fibers over rational points

Extension of Chevalley-Weil theorem to explicit dimension-one case

Improved understanding of field of definition discriminants in algebraic geometry

Abstract

The classical Chevalley-Weil theorem asserts that for an \'etale covering of projective varieties over a number field K, the discriminant of the field of definition of the fiber over a K-rational point is uniformly bounded. We obtain a fully explicit version of this theorem in dimension 1.