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• W2094582135 abstract "Let M be an overconvergent isocrystal on a smooth affine curve X/k over a perfect field of characteristic p > 0, realized as a module on a suitable lifting of X with connection. We give a topological condition on the connection which guarantees that the rigid cohomology of M is finite-dimensional. As a result, one sees that M has finite-dimensional cohomology if it satisfies an analogue of Grothendieck's local monodromy theorem. Some arithmetic applications are given. Soit M un isocristal surconvergent sur une courbe X/k affine et lisse sur un corps parfait de caractéristique p > 0, réalisé comme module à connexion sur un relèvement convenable de X. Nous donnons une condition de nature topologique sur la connexion pour que la cohomologie rigide de M soit de dimension finie. Il en résulte que la cohomologie de M sera de dimension finie si M vérifie une analogue du théorème de monodromie locale de Grothendieck. On donne aussi des applications arithmétiques de ce résultat." @default.
• W2094582135 created "2016-06-24" @default.
• W2094582135 creator A5072485475 @default.
• W2094582135 date "1998-11-01" @default.
• W2094582135 modified "2023-09-25" @default.
• W2094582135 title "Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve" @default.
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• W2094582135 doi "https://doi.org/10.1016/s0012-9593(99)80001-9" @default.
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