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 (eng) | 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 . - Société Mathématique de France, 1994 . - 183 p.. - ( Astérisque, ISSN 0303-1179; 221) . Langues : Anglais ( eng) 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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