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Explicit Frobenius descent for \({\mathcal D}^\dagger\)-modules. (Descente par Frobenius explicite pour les \({\mathcal D}^\dagger\)-modules.) (French) Zbl 0926.12006

The purpose of this paper is to give explicit and global formulae for Frobenius decent of \({\mathcal D}_{\mathcal X}^\dagger\)-modules. This completes Berthelot theory. The main argument developed here is an interpretation of the Dwork \(\psi\) function as an infinite differential operator. Applications are given, in this paper to Cartier isomorphism and Cartier operator, and in another paper to new proofs of Christol main theorems (about indexes of differential operators).

MSC:

12H25 \(p\)-adic differential equations
14F30 \(p\)-adic cohomology, crystalline cohomology
14G20 Local ground fields in algebraic geometry
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