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The cohomology of Monsky and Washnitzer. (English) Zbl 0606.14018
The paper gives a very nice introduction to Monsky-Washnitzer cohomology. It begins by the definition of MW cohomology and some of its basic properties, such as construction of the Frobenius map and the Lefschetz fixed point formula for it. The exposition has been simplified and somewhat extended with the aid of the Artin approximation theorem and some rigid analysis. The article then goes on to describe some more specific topics and ends by discussing Dwork’s work on the cohomology of the family of elliptic curves, its unit root part etc. This article can be recommended as a short introduction to anyone interested in these subjects.
Reviewer: T.Ekedahl

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
14G20 Local ground fields in algebraic geometry
14B12 Local deformation theory, Artin approximation, etc.
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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References:
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