F-isocrystals and de Rham cohomology. II: Convergent isocrystals
[For part I see \textit{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.
scientific article; zbMATH DE number 3935197
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