An Effective Version of Chevalley-Weil Theorem for Projective Plane Curves

Abstract

We obtain a quantitative version of the classical Chevalley-Weil theorem for curves. Let $\varphi :\tilde{C}\to C$ be an unramified morphism of non-singular plane projective curves defined over a number field $K$. We calculate an effective upper bound for the norm of the relative discriminant of the number field $K(Q)$ over $K$ for any point $P\in C(K)$ and $Q\in {\varphi }^{-1}(P)$