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F-crystals, Griffiths transversality and the Hodge decomposition / Arthur Ogus

Auteur principal : Ogus, Arthur, 1945-, AuteurType de document : MonographieCollection : Astérisque, 221Langue : anglais.Pays : France.Éditeur : Paris : Société Mathématique de France, 1994Description : 1 vol. (183 p.) ; 24 cmISSN : 0303-1179.Bibliographie : Bibliogr. p. 181-183.Sujet MSC : 14F30, (Co)homology theory in algebraic geometry, p-adic cohomology, crystalline cohomology
14C30, Algebraic geometry - Cycles and subschemes, Transcendental methods, Hodge theory, Hodge conjecture
14-02, Research exposition (monographs, survey articles) pertaining to algebraic geometry
14D07, Families, fibrations in algebraic geometry, Variation of Hodge structures
En-ligne : Résumé
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Séries SMF 221 (Browse shelf) Available 11140-01

The book gives a systematic treatment of phenomena arising from the divisibility of Frobenius by powers of p. For crystalline cohomology with constant coefficients this goes back to Mazur, but more recently the work of Fontaine-Lafaille and others lead to a definition of more general coefficients. Their special cases were treated at hoc. The bulk of the book consists of various types of fitrations and their compatibilities. This is then applied to crystalline cohomology, and applications like degeneration of spectral sequences are given. There are also some consequences for modular forms, but the author seems to promise more exhausting treatment of that subject for a later time. (Zentralblatt)

Bibliogr. p. 181-183

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