In order to give a formal treatment of differential equations in positive characteristic p, it is necessary to use divided powers. One runs into an analog problem in the theory of q-difference equations when q is a pth root of unity. We introduce here a notion of twisted divided powers (relative to q) and show that one can recover the twisted Weyl algebra and obtain a twisted p-curvature map that describes the center of the twisted Weyl algebra. We also build a divided p-Frobenius that will give, by duality, a formal Azumaya splitting of the twisted Weyl algebra as well as a twisted Simpson correspondence.

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扭曲的分权和应用

为了对正特征p中的微分方程进行形式化处理，有必要使用除幂。当q是第 p个单位根时，我们会在q差分方程的理论中遇到一个模拟问题。我们在此引入了扭曲除幂（相对于q）的概念，并表明可以恢复扭曲的外尔代数并获得描述扭曲外尔代数中心的扭曲p曲率图。我们还构建了一个分裂的p -Frobenius，它通过对偶给出扭曲的 Weyl 代数的正式 Azumaya 分裂以及扭曲的 Simpson 对应。