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Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve

Identifieur interne : 002514 ( Istex/Corpus ); précédent : 002513; suivant : 002515

Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve

Auteurs : Richard Crew

Source :

RBID : ISTEX:B3C2CB18C2188ED86DFFF073C77A49126D0C4C37

English descriptors

Abstract

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.

Url:
DOI: 10.1016/S0012-9593(99)80001-9

Links to Exploration step

ISTEX:B3C2CB18C2188ED86DFFF073C77A49126D0C4C37

Le document en format XML

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<div type="abstract" xml:lang="en">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.</div>
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