Morphisms of F-isocrystals and the Finite Monodromy Theorem for Unit-root F-isocrystals
نویسنده
چکیده
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.
منابع مشابه
Semistable reduction for overconvergent F -isocrystals, III: Local semistable reduction at monomial valuations
We resolve the local semistable reduction problem for overconvergent F -isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree 0). We first introduce a higher-dimensional analogue of the generic radius of convergence for a p-adic differential module, which obeys a convexity property. We then combine this convexity property with a form of the p-adic...
متن کاملSemistable reduction for overconvergent, F-isocrystals, III: Local semistable reduction at monomial valuations Citation
We resolve the local semistable reduction problem for overconvergent F -isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree zero). We first introduce a higher-dimensional analogue of the generic radius of convergence for a p-adic differential module, which obeys a convexity property. We then combine this convexity property with a form of the p-a...
متن کاملOverholonomicity of overconvergent F-isocrystals over smooth varieties
We prove the overholonomicity of overconvergent F-isocrystals over smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent F-isocrystals are equivalent. Then the overholonomicity is stable under tensor products. So, the overholonomicity gives a p-adic cohomology stable under Grothendieck’s cohomological operations.
متن کاملF–isocrystals and Homotopy Types (f–isocristaux Et Types D’homotopie)
We study a positive characteristic analog of the nonabelian Hodge structure constructed by Katzarkov, Pantev, and Toen on the homotopy type of a complex algebraic variety. Given a proper smooth scheme X over a perfect field of characteristic p and a Tannakian category C of isocrystals on X, we construct an object XC in a suitable homotopy category of simplicial presheaves whose category of loca...
متن کاملSemistable Reduction of overconvergent F -isocrystals I: Isocrystals and Rigid Cohomology
Notation 1.1.2. By a k-variety, I meant a reduced (not necessarily irreducible) separated scheme of finite type over k. (It could be shown that the theory only depends on the reduced scheme structure.) Through out the talk, X will be an open subscheme of a k-variety Y and Z = X\Y is the complement with the reduced scheme structure. P will always denote a topologically finite type formal scheme ...
متن کامل