Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
Identifieur interne : 002514 ( Istex/Corpus ); précédent : 002513; suivant : 002515Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
Auteurs : Richard CrewSource :
- Annales scientifiques de l'Ecole normale superieure [ 0012-9593 ] ; 1998.
English descriptors
- KwdEn :
- Affine, Affinoid, Algebra, Algebraic, Algebraic closure, Annales, Annales scientifiques, Archimedean case, Banach, Banach space, Banach spaces, Barreled, Barreled spaces, Berthelot, Bezout ring, Bornological, Closure, Cohomologie, Cohomologie rigide, Cohomology, Coker, Commutative diagram, Compact sets, Compact subset, Conjugacy classes, Convex, Convex sets, Convex space, Corresponding module, Countable, Direct image, Direct limit, Direct summand, Discretely, Divisor, Duality, Eigenvalue, Embedding, Endomorphism, Equicontinuous, Exact sequence, Fiber functor, Filtration, Finite, Finite extension, Finite presentation, Finite rank, Finite type, Finite union, Finitely, Finiteness, Finiteness theorems, Formal laurent series, Frechet, Frechet space, Frechet spaces, Free sheaf, Frobenius, Frobenius structure, Functional analysis, Functor, Global pairing, Inductive, Inductive limit, Injective, Inverse limit, Isocrystal, Isocrystals, Isomorphic, Isomorphism, Jinite, Laurent, Lecture notes, Linear compactness, Liouville, Local algebra, Local algebras, Local duality, Local pairing, Local parameter, Local section, Main result, Module, Monodromy, Monte1, Monte1 space, Monte1 spaces, Morphism, Natural topology, Nilpotent endomorphism, Normale, Normale superieure, Open mapping theorem, Open neighborhood, Open subset, Other hand, Overconvergent, Overconvergent isocrystal, Pairing, Priifer ring, Quotient, Reflexive, Resp, Rham cohomology, Rigid cohomology, Rigide, Same argument, Scientifiques, Serre, Serre duality, Sheaf, Smooth affine curve, Smooth compactification, Smooth curve, Smooth curves, Strict, Strict isocrystal, Strict neighborhood, Strict neighborhoods, Strictness, Subset, Successive extension, Summand, Surjective, Tome, Topological, Topological isomorphism, Topological isomorphisms, Topological spaces, Topology, Transpose, Unipotent, Unipotent connection, Value group, Vector space.
- Teeft :
- Affine, Affinoid, Algebra, Algebraic, Algebraic closure, Annales, Annales scientifiques, Archimedean case, Banach, Banach space, Banach spaces, Barreled, Barreled spaces, Berthelot, Bezout ring, Bornological, Closure, Cohomologie, Cohomologie rigide, Cohomology, Coker, Commutative diagram, Compact sets, Compact subset, Conjugacy classes, Convex, Convex sets, Convex space, Corresponding module, Countable, Direct image, Direct limit, Direct summand, Discretely, Divisor, Duality, Eigenvalue, Embedding, Endomorphism, Equicontinuous, Exact sequence, Fiber functor, Filtration, Finite, Finite extension, Finite presentation, Finite rank, Finite type, Finite union, Finitely, Finiteness, Finiteness theorems, Formal laurent series, Frechet, Frechet space, Frechet spaces, Free sheaf, Frobenius, Frobenius structure, Functional analysis, Functor, Global pairing, Inductive, Inductive limit, Injective, Inverse limit, Isocrystal, Isocrystals, Isomorphic, Isomorphism, Jinite, Laurent, Lecture notes, Linear compactness, Liouville, Local algebra, Local algebras, Local duality, Local pairing, Local parameter, Local section, Main result, Module, Monodromy, Monte1, Monte1 space, Monte1 spaces, Morphism, Natural topology, Nilpotent endomorphism, Normale, Normale superieure, Open mapping theorem, Open neighborhood, Open subset, Other hand, Overconvergent, Overconvergent isocrystal, Pairing, Priifer ring, Quotient, Reflexive, Resp, Rham cohomology, Rigid cohomology, Rigide, Same argument, Scientifiques, Serre, Serre duality, Sheaf, Smooth affine curve, Smooth compactification, Smooth curve, Smooth curves, Strict, Strict isocrystal, Strict neighborhood, Strict neighborhoods, Strictness, Subset, Successive extension, Summand, Surjective, Tome, Topological, Topological isomorphism, Topological isomorphisms, Topological spaces, Topology, Transpose, Unipotent, Unipotent connection, Value group, Vector space.
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
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<front><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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<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.</abstract>
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<abstract xml:lang="en"><p>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.</p>
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<abstract xml:lang="fr"><p>Résumé: 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.</p>
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<head><ce:title>Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve</ce:title>
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<ce:abstract-sec><ce:simple-para>Let <ce:italic>M</ce:italic>
be an overconvergent isocrystal on a smooth affine curve <ce:italic>X</ce:italic>
/<ce:italic>k</ce:italic>
over a perfect field of characteristic <ce:italic>p</ce:italic>
> 0, realized as a module on a suitable lifting of <ce:italic>X</ce:italic>
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has finite-dimensional cohomology if it satisfies an analogue of Grothendieck's local monodromy theorem. Some arithmetic applications are given.</ce:simple-para>
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un isocristal surconvergent sur une courbe <ce:italic>X</ce:italic>
/<ce:italic>k</ce:italic>
affine et lisse sur un corps parfait de caractéristique <ce:italic>p</ce:italic>
> 0, réalisé comme module à connexion sur un relèvement convenable de <ce:italic>X</ce:italic>
. Nous donnons une condition de nature topologique sur la connexion pour que la cohomologie rigide de <ce:italic>M</ce:italic>
soit de dimension finie. Il en résulte que la cohomologie de <ce:italic>M</ce:italic>
sera de dimension finie si <ce:italic>M</ce:italic>
vérifie une analogue du théorème de monodromie locale de Grothendieck. On donne aussi des applications arithmétiques de ce résultat.</ce:simple-para>
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<abstract 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.</abstract>
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