| 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 |
|
Affiner la recherche Interroger des sources externesF-crystals, Griffiths transversality, and the Hodge decomposition / Arthur OGUS (1994)
