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Géométrie rigide et cohomologie des variétés algébriques de \(caract\acute eristique\quad p\). (Rigid geometry and cohomology of algebraic varieties of \(characteristic\quad p\)). (French) Zbl 0606.14017
The author gives the basic definitions concerning rigid analytic cohomology, a common generalisation of crystalline cohomology (up to isogeny) and Monsky-Washnitzer cohomology. Among other things he introduces rigid cohomology with compact supports and shows that one has the expected exact sequences, hence giving finiteness results for all varieties which can be embedded in a smooth and proper variety with normal crossing complement. He ends by introducing the notion of overconvergent crystals, the proposed local coefficient systems of the theory.
Reviewer: T.Ekedahl

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