Morphisms of F-isocrystals and the finite monodromy theorem for unit-root F-isocrystals

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 overc...

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Bibliographic Details
Published in:Duke mathematical journal 2002-02, Vol.111 (3), p.385-418
Main Author: Tsuzuki, Nobuo
Format: Article
Language:English
Subjects:
11G25
14F10
14F30
14G20
32C38
Bernstein-Sato ideals and polynomials [See also 13Nxx
crystalline cohomology
D-modules
Differentials and other special sheaves
p$-adic cohomology
Varieties over finite and local fields [See also 14G15
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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.
ISSN:0012-7094
1547-7398
DOI:10.1215/s0012-7094-02-11131-4