AI 中文总结
该研究在任意特征下建立有限线性约化群概型的动机与上同调McKay对应，推广Artin栈动机积分理论，证明平展解消欧拉数等于群不可约表示数的结论。
AI 中文摘要
我们得到了任意特征下有限线性约化群概型的动机McKay对应与上同调McKay对应。特别地，若V是有限维向量空间，G是SL(V)的有限线性约化子群概型，则V/G的任意平展解消的欧拉数等于G的不可约代数表示的个数。我们将这些McKay对应作为应用于[V/G]→V/G的动机变量替换公式的推论得到。若G是非约化的（正特征下可能出现），栈商[V/G]不是Deligne-Mumford的。因此，为证明该变量替换公式及由此得到的McKay对应，我们将作者的Artin栈动机积分理论推广到任意特征，这一工作可能具有独立意义。
英文摘要
We obtain a motivic and a cohomological McKay correspondence for finite linearly reductive group schemes in arbitrary characteristic. In particular, we prove that if $V$ is a finite dimensional vector space and $G$ is a finite linearly reductive subgroup scheme of $\mathrm{SL}(V)$, then the Euler number of any crepant resolution of $V/G$ is equal to the number of irreducible algebraic representations of $G$. We obtain these McKay correspondences as a consequence of a motivic change of variables formula applied to $[V/G] \to V/G$. If $G$ is non-reduced, as can happen in positive characteristic, the stack quotient $[V/G]$ is not Deligne-Mumford. Therefore in order to prove this change of variables formula and the resulting McKay correspondences, we generalize the authors' theory of motivic integration for Artin stacks to arbitrary characteristic, which may be of independent interest.
