Twisted divided powers and applications
EntityUAM. Departamento de Matemáticas
10.1016/j.jnt.2019.02.009Journal of Number Theory 237 (2022): 285-331
ProjectGobierno de España. MTM2015-68524-P
SubjectsDivided Frobenius; p-Curvature; Divided Power; Positive Characteristic; q-Difference Equation; Simpson Correspondence; Weyl Algebra; Matemáticas
Rights© 2019 Elsevier Inc.
Esta obra está bajo una Licencia Creative Commons Atribución 4.0 Internacional.
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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