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Article Dans Une Revue Journal of Number Theory Année : 2019

Twisted divided powers and applications

Résumé

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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Dates et versions

hal-01629477 , version 1 (06-11-2017)

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Michel Gros, Bernard Le Stum, Adolfo Quirós. Twisted divided powers and applications. Journal of Number Theory, 2019, 237, pp.285-331. ⟨10.1016/j.jnt.2019.02.009⟩. ⟨hal-01629477⟩
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