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Morphisms of \(F\)-isocrystals and the finite monodromy theorem for unit-root \(F\)-isocrystals. (English) Zbl 1055.14022
Summary: We discuss Tate-type problems for \(F\)-isocrystals, that is, the full faithfulness of the natural restriction functors between categories of overconvergent \(F\)-isocrystals on schemes of positive characteristic. We prove it in the cases of unit-root \(F\)-isocrystals. Using this result, we prove that an overconvergent unit-root \(F\)-isocrystal has a finite monodromy.

MSC:
14F30 \(p\)-adic cohomology, crystalline cohomology
11G25 Varieties over finite and local fields
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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