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Une introduction naïve aux cohomologies de Dwork. (A naïve introduction to Dwork cohomology). (French) Zbl 0623.14005

In Dwork’s original work on the Zeta-function of algebraic varieties one finds the beginning of a cohomology theory. This theory has been worked out by Monsky and Washnitzer. A unification with cristalline cohomology is given by Berthelot. In the present paper a didactical effort is made to present this “Dwork cohomology” in its naive form. The cohomology is associated to a differential equation. On the cohomology one considers Frobenius-structure, variation etc. Classical equations as Bessel equation, hypergeometric equations are given as examples. The relations with Zeta-functions and L-functions is given.
Reviewer: M.van der Put

MSC:

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