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arXiv · 1711.01907

Twisted divided powers and applications

Michel Gros·Bernard Le Stum·Adolfo Quirós
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Abstract

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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Michel Gros, Bernard Le Stum, Adolfo Quirós. 2017-11-06. Twisted divided powers and applications. https://arxiv.org/abs/1711.01907

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