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F-isocrystals and de Rham cohomology. II: Convergent isocrystals. (English) Zbl 0584.14008
[For part I see P. Berthelot and the author, Invent. Math. 72, 159- 199 (1983; Zbl 0516.14017).]
The author studies the relation between de Rham and crystalline cohomology for a smooth proper map of flat V-schemes (V a complete discrete valuation ring with fraction field of characteristic 0 and residue field of characteristic \(p>0).\) For this the notion of convergent isocrystal (a collection of sheaves on certain ”thickenings” of schemes over \({\mathbb{Z}})\) is introduced and used to study p-adic analytic continuation. The main application shows the compatibility of the absolute Hodge cycle linking a K3 surface to its Kuga-Satake abelian variety with the action of Frobenius on crystalline cohomology.
Reviewer: P.Cherenack

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
14F40 de Rham cohomology and algebraic geometry
14G20 Local ground fields in algebraic geometry
14D99 Families, fibrations in algebraic geometry
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