Quantitative Chevalley-Weil theorem for curves

Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem

We prove an analogue for algebraic stacks of Hermite-Minkowski's finiteness theorem from algebraic number theory, and establish a Chevalley-Weil type theorem for integral points on stacks. As an application of our results, we prove analogues of the Shafarevich conjecture for some surfaces of general type.

Around the Chevalley-Weil Theorem

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.

The Chevalley-Weil Formula for Orbifold Curves

In the 1930s Chevalley and Weil gave a formula for decomposing the canonical representation on the space of differential forms of the Galois group of a ramified Galois cover of Riemann surfaces. In this article we prove an analogous Chevalley-Weil formula for ramified Galois covers of orbifold curves. We then specialize the formula to the case when the base orbifold curve is the (reduced) modular orbifold. As an application of this latter formula we decompose the canonical representations of modular curves of full, prime level and of Fermat curves of arbitrary exponent.

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

We obtain a quantitative version of the classical Chevalley-Weil theorem for curves. Let $ϕ: \tilde{C} \to C$ 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 $Q\inϕ^{-1}(P)$

Chevalley-Weil Theorem and Subgroups of Class Groups

We prove, under some mild hypothesis, that an étale cover of curves defined over a number field has infinitely many specializations into an everywhere unramified extension of number fields. This constitutes an "absolute" version of the Chevalley-Weil theorem. Using this result, we are able to generalize the techniques of Mestre, Levin and the second author for constructing and counting number fields with large class group.

曲线上 $\mathbf{P}^n$-丛中超曲面的 Chevalley-Weil 公式与函数域塔中的 Mordell-Weil 秩

Chevalley-Weil formula for hypersurfaces in $\mathbf{P}^n$-bundles over curves and Mordell-Weil ranks in function field towers

本文研究曲线上射影丛中超曲面在 Galois 基变换下的 Hodge 上同调群结构，给出 Chevalley-Weil 型公式，并借此几何证明椭圆曲面 Mordell-Weil 秩的 Pal 上界，同时比较其与 Shioda-Tate 公式界的强弱关系。