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F-crystals, Griffiths transversality, and the Hodge decomposition / Arthur OGUS (1994)

Public ISBD Titre : F-crystals, Griffiths transversality, and the Hodge decomposition Type de document : texte imprimé Auteurs : Arthur OGUS, Auteur Editeur : Paris : Société Mathématique de France Année de publication : 1994 Collection : Astérisque, ISSN 0303-1179 num. 221 Importance : 183 p. Langues : Anglais Catégories : 11G25 14C30 14D07 14F17 14F30 Mots-clés : structure logarithmique  filtration  bifiltration  étalon  cohomologie cristalline  théorème de Mazur Résumé : Pursuing the analogy between variations of Hodge structures in characteristic zero and F-crystals in characteristic p, we introduce and study the category of ``T-crystals", which are the crystalline manifestation of modules with integrable connection and filtration satisfying Griffiths transversality. We construct a functor from the category of F-crystals (or more generally F-spans) to the category of T-crystals, on any smooth logarithmic scheme in characteristic p. This functor is shown to commute with the formation of higher direct images-a generalization of Mazur's fundamental theorem on Frobenius and Hodge filtration to the case of crystalline cohomology with coefficients. Applications include results about Newton and Hodge polygons (``Katz's Conjecture'') and the degeneration of the Hodge spectral sequence (``Hodge Decomposition''), in both cases for the cohomology of a variety with coefficients in an F-crystal. Note de contenu : références F-crystals, Griffiths transversality, and the Hodge decomposition [texte imprimé] / Arthur OGUS, Auteur . - Paris : Société Mathématique de France, 1994 . - 183 p.. - (Astérisque, ISSN 0303-1179; 221) . Langues : Anglais Catégories : 11G25 14C30 14D07 14F17 14F30 Mots-clés : structure logarithmique  filtration  bifiltration  étalon  cohomologie cristalline  théorème de Mazur Résumé : Pursuing the analogy between variations of Hodge structures in characteristic zero and F-crystals in characteristic p, we introduce and study the category of ``T-crystals", which are the crystalline manifestation of modules with integrable connection and filtration satisfying Griffiths transversality. We construct a functor from the category of F-crystals (or more generally F-spans) to the category of T-crystals, on any smooth logarithmic scheme in characteristic p. This functor is shown to commute with the formation of higher direct images-a generalization of Mazur's fundamental theorem on Frobenius and Hodge filtration to the case of crystalline cohomology with coefficients. Applications include results about Newton and Hodge polygons (``Katz's Conjecture'') and the degeneration of the Hodge spectral sequence (``Hodge Decomposition''), in both cases for the cohomology of a variety with coefficients in an F-crystal. Note de contenu : références

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
15981	AST 221	Livre	Recherche	Salle	Disponible