A note on effective descent for overconvergent isocrystals
نویسندگان
چکیده
منابع مشابه
Semistable reduction for overconvergent F -isocrystals on a curve
Let X be a smooth affine curve over a field k of characteristic p > 0 and E an overconvergent F a-isocrystal on X for some positive integer a. We prove that after replacing k by some finite purely inseparable extension, there exists a finite separable morphism X ′ → X, the pullback of E along which extends to a log-F a-isocrystal on a smooth compactification of X . This resolves a weak form of ...
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Background Cohomological descent is a robust computational and theoretical tool, central to p-adic cohomology and its applications. On the one hand, it facilitates explicit calculations (analogous to the computation of coherent cohomology in scheme theory via Čech cohomology); on the other, it allows one to deduce results about singular schemes (e.g., finiteness of the cohomology of overconverg...
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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.
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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 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 ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.09.014