A differential analog of a theorem of Chevalley

A differential Chevalley theorem

We prove a differential analog of a theorem of Chevalley on extending homomorphisms for rings with commuting derivations, generalizing a theorem of Kac. As a corollary, we establish that, under suitable hypotheses, the image of a differential scheme under a finite morphism is a constructible set. We also obtain a new algebraic characterization of differentially closed fields. We show that similar results hold for differentially closed fields that are saturated, in the sense of model theory. In characteristic p > 0, we obtain related results and establish a differential Nullstellensatz. Analogs…

节点曲线上的 Chevalley-Weil 公式

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。

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.

A uniform Chevalley theorem for direct summands of polynomial rings in mixed characteristic

We prove an explicit uniform Chevalley theorem for direct summands of graded polynomial rings in mixed characteristic. Our strategy relies on the introduction of a new type of differential powers, which do not require the existence of a p-derivation on the direct summand.

A Chevalley theorem for difference equations

By a theorem of Chevalley the image of a morphism of varieties is a constructible set. The algebraic version of this fact is usually stated as a result on "extension of specializations" or "lifting of prime ideals". We present a difference analog of this theorem. The approach is based on the philosophy that occasionally one needs to pass to higher powers of $σ$, where $σ$ is the endomorphism defining the difference structure. In other words, we consider difference pseudo fields (which are finite direct products of fields) rather than difference fields. We also prove a result on compatibility o…

Peterson-Lam-Shimozono 定理是量子 Chevalley 公式的仿射类比

Peterson-Lam-Shimozono's theorem is an affine analogue of quantum Chevalley formula

本文为Peterson-Lam-Shimozono定理提供新证明，通过构造并识别Gromov-Witten理论中的代数同态为Peterson映射，完全确定了联系旗簇等变量子同调与仿射Grassmannian等变Pontryagin同调的结构常数。