Donu Arapura
Given a finite group of automorphisms of a compact Riemann surface, the Chevalley-Weil formula computes the character valued Euler characteristic of an equivariant line bundle. The goal of this article is to give a proof by computing using residues of a Gauss-Manin connection.
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The Chevalley-Weil formula on nodal curves
本文研究了代数闭域上节点曲线全纯微分空间在有限自同构群作用下的特征子空间，在商曲线附加条件下计算了 Chevalley-Weil 公式并给出实例。
In our previous paper, we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed field of characteristic 0 with genus $g>1$, Nori fundamental group acts faithfully on the unipotent fundamental group of its universal covering. However, it was not mentioned about any explicit module structure. In this paper, we prove that the Chevalley-Weil formula gives a description of it.
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.
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.
Quantitative Chevalley-Weil theorem for curves
经典的Chevalley-Weil定理断言，对于数域K上的投射簇的一个代数覆盖，K-有理点上纤维的定义域的判别式是一致有界的。我们得到一个完全明确的版本，这个定理在1维。
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
我们得到一个定量版本的经典Chevalley-Weil定理的曲线。设$ϕ: \tilde{C} \to C$是数域$K$上非奇异平面射影曲线的非分歧态射.我们计算了数域$K(Q)$对$K$的相对判别式对任意点$P\in C(K)$和$Q\inϕ^{-1}(P)$的模的有效上界
This paper shows how the Theorem of Residues (TR) and the Gelfand-Fuchs cocycle can be deduced in a simple way from the Weil Reciprocity Law (WRL). Indeed, if one understand WRL as the triviality of certain extension of groups, then TR is the same statement at the level of Lie algebras. Finally, the Gelfand-Fuchs cocycle can also be obtained in this way.
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。
Geometric Realization of Finite Residue Casimirs and Weil Operators via Szegő Kernels
本文针对有限域上带无穷远点的光滑射影曲线，通过Szegő核实现有限剩余卡西米尔与Weil算子的几何化，为相关配对研究提供了几何基础。
The Chevalley--Weil formula for finite group actions on higher dimensional compact complex manifolds
本文基于 Atiyah--Singer 全纯 Lefschetz 不动点定理定义了分歧模，将紧 Riemann 面的 Chevalley--Weil 公式推广至高维紧复流形上的有限群作用，并给出了相关公式与计算实例。
We reinterpret the residue map for the Brauer group of a smooth variety using a root stack construction and Weil restriction for algebraic stacks, and apply the result to find a geometric representative of for the residue of a Brauer class associated to a conic bundle, or more generally a Brauer-Severi bundle.
Computing the equivariant Euler characteristic of Zariski and etale sheaves on curves
证明了一个等变的Grothendieck-Ogg-Shafarevich公式。这个公式可以被看作是一个著名的公式的经典类似物，推广了经典的Chevalley-Weil公式。我们给出了一个新的方法，这些公式（首先证明了Ellingsrud/Lønsted，Nakajima，Kani和Ksir），也可以应用在étale的情况下。
On the cohomological representations of finite automorphism groups of singular curves and compact complex spaces
本文研究了有限群作用下奇异曲线和紧复空间的上同调表示，推导了Chevalley--Weil型公式，并探讨了节点曲线的不变截面和变形空间。
Computing the Weil representation of a superelliptic curve
本文研究p-进域上具有紧型潜在约化的曲线的Weil表示，证明其可由稳定约化重构，并对剩余特征与指数n互素的超椭圆曲线y^n=f(x)给出显式计算方法。
Weil's Theorem for Logarithmic Connections on Irreducible Nodal Curves
本研究将André Weil经典定理推广至不可约射影结点曲线，证明其上不可分解向量丛或无挠凝聚层存在关于对偶化层的全纯对数联络等价于次数为0，还构造了有理结点三次曲线上的显式单参数平坦联络族。
An old theorem of Weil and Kodaira says that for a compact Kähler manifold $X$ there is a closed logarithmic $1$-form with residue divisor $D$ if and only if $D$ is homologous to zero in $H_{2n-2}(X,\mathbb C)$. In the first part of this paper, we generalize the above theorem to general compact complex manifolds by showing that the necessary and sufficient condition in general is described by a holomorphic invariant called the $\mathcal Q$-flat class. Next, we prove that the holomorphic criterion is reduced to the topological one when $X$ has Property $(H)$. Since all Kähler manifolds have Pro…
Weil groups and $F$-isocrystals
本文从特征 $p>0$ 代数闭域上 $F$-isocrystals 的 Dieudonné-Manin 结构理论推导局部类域论，给出了范数剩余符号 Dwork 公式及局部 Shafarevich-Weil 定理的新证明，并回答了 Morava 的问题。
A theorem of Weil and Atiyah says that a holomorphic vector bundle $E$ on a compact Riemann surface $X$ admits a holomorphic connection if and only if the degree of every direct summand of $E$ is zero. Fix a finite subset $S$ of $X$, and fix an endomorphism $A(x) \in \text{End}(E_x)$ for every $x \in S$. It is natural to ask when there is a logarithmic connection on $E$ singular over $S$ with residue $A(x)$ at every $x \in S$. We give a necessary and sufficient condition for it under the assumption that the residues $A(x)$ are rigid.
Let $f:X \to S$ be a Galois cover of Riemann surfaces, with Galois group $G$. In this paper we analyze the $G$-invariant divisors on $X$, and their associated spaces of meromorphic functions, differentials, and $q$-differentials. We generalize the trace formula for non-trivial elements of $G$ on $q$-differentials, as well as the Chevalley--Weil Formula. When $G$ is Abelian or when the genus of $S$ is 0 we prove additional results, and we also determine the non-special $G$-invariant divisors when both conditions are satisfied.
The de Rham cohomology of covers with cyclic $p$-Sylow subgroup
本文证明了当有限群 $G$ 具有循环 $p$-Sylow 子群时，光滑射影曲线 $X$ 的 de Rham 上同调的 $G$-结构完全由分歧数据决定，并在两种特定情形下给出了显式公式。
On Weil Polynomials of Hyperelliptic Curves over Finite Fields of Characteristic 2
本文通过模2剩余类约束给出特征2有限域上超椭圆雅可比矩阵存在性的新阻碍条件，证明Weil系数奇偶性渐近等分布，并据此排除大量3维和4维同源类，同时提出运行时间显著改进的任意亏格超椭圆曲线枚举算法。
We review, under a perspective which appears different from previous ones, the so-called Hilbert Property (HP) for an algebraic variety (over a number field); this is linked to Hilbert's Irreducibility Theorem and has important implications, for instance towards the Inverse Galois Problem. We shall observe that the HP is in a sense `opposite' to the Chevalley-Weil Theorem, which concerns unramified covers; this link shall immediately entail the result that the HP can possibly hold only for simply connected varieties (in the appropriate sense). In turn, this leads to new counterexamples to the …
Distribution of the traces of Frobenius on elliptic curves over function fields
设C是定义在特征p>3的q元有限域$\mathbb{F}_{q}$上的光滑不可约射影曲线，$K=\mathbb{F}_{q}(C)$是它的函数域，$ϕ_{\mathcal{E}}:\mathcal{E}\to C$是$\mathbf{E}/K$的极小正则模型.对于每个$P\in C$，表示为$\mathcal{E}_P=ϕ^{-1}_{\mathcal{E}}(P)$。椭圆曲线$E/K$在$P\in C$上有良好的约简当且仅当$\mathcal{E}_P$是定义在$P$的剩余域$κ_P$上的椭圆曲线。这个域是$\mathbb{F}_q$的次数为$°(P)$的有限扩张。设$t(\mathcal{E}_P)=q^{°(P)}+1-#\mathcal{E}_P(κ_P)$是Frobenius在P处的迹。[10，第五章，定理2.4]），则$t(\mathcal{E}_P)$是$\mathcal{E}_P$的zeta函数的零点的逆的和。特别是$|t(\mathcal{E}_P)|\le 2q^{°(P)}$。设$C_0\subset C$是C中$E/K$具有良好约化的点集，$C_0(\mathbb{F}_{q^k})$是$C_0$的$\mathbb{F}_{q^k}$ -有理点的子集.我们讨论以下问题。设$k\ge 1$和t是整数，并假设$|t|\le 2q^{k/2}$。设$π(k,t)=…
On Bruhat-Tits theory over a higher dimensional base
本文推广Bruhat-Tits理论到高维基，通过定义n-有界子群并证明其可模式化，构造了适应正规交叉除数的群概形，并给出了在特征零中的应用。
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