Specialization of crystalline cohomology. (English) Zbl 0615.14010

Let \(f: X\to S\) be a proper smooth morphism of schemes over a perfect field of characteristic \(p\). Using the theory of convergent isocrystals, it is shown that the Newton polygons of the \({\mathbb{Q}}\otimes H^ i_{cris}(X_ s/W(s))\) (the relative crystalline cohomology of a fiber) are constant along the strata of a suitable stratification of A and rise under specialization.
Reviewer: J.H.de Boer


14F30 \(p\)-adic cohomology, crystalline cohomology
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