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- Dieudonné_module abstract "In mathematics, a Dieudonné module introduced by Dieudonné (1954, 1957b), is a module over the non-commutative Dieudonné ring, which is generated over the ring of Witt vectors by two special endomorphisms F and V called the Frobenius and Verschiebung operators. They are used for studying finite flat commutative group schemes.Finite flat commutative group schemes over a perfect field k of positive characteristic p can be studied by transferring their geometric structure to a (semi-)linear-algebraic setting. The basic object is the Dieudonné ring D = W(k){F,V}/(FV − p), which is a quotient of the ring of noncommutative polynomials, with coefficients in Witt vectors of k. F and V are the Frobenius and Verschiebung operators, and they may act nontrivially on the Witt vectors. Jean Dieudonné and Pierre Cartier constructed an antiequivalence of categories between finite commutative group schemes over k of order a power of "p" and modules over D with finite W(k)-length. The Dieudonné module functor in one direction is given by homomorphisms into the abelian sheaf CW of Witt co-vectors. This sheaf is more or less dual to the sheaf of Witt vectors (which is in fact representable by a group scheme), since it is constructed by taking a direct limit of finite length Witt vectors under successive Verschiebung maps V: Wn → Wn+1, and then completing. Many properties of commutative group schemes can be seen by examining the corresponding Dieudonné modules, e.g., connected p-group schemes correspond to D-modules for which F is nilpotent, and étale group schemes correspond to modules for which F is an isomorphism.Dieudonné theory exists in a somewhat more general setting than finite flat groups over a field. Oda's 1967 thesis gave a connection between Dieudonné modules and the first de Rham cohomology of abelian varieties, and at about the same time, Grothendieck suggested that there should be a crystalline version of the theory that could be used to analyze p-divisible groups. Galois actions on the group schemes transfer through the equivalences of categories, and the associated deformation theory of Galois representations was used in Wiles's work on the Shimura–Taniyama conjecture.".
- Dieudonné_module wikiPageExternalLink cartier1.pdf.
- Dieudonné_module wikiPageID "27127074".
- Dieudonné_module wikiPageLength "6493".
- Dieudonné_module wikiPageOutDegree "15".
- Dieudonné_module wikiPageRevisionID "575146780".
- Dieudonné_module wikiPageWikiLink American_Journal_of_Mathematics.
- Dieudonné_module wikiPageWikiLink Andrew_Wiles.
- Dieudonné_module wikiPageWikiLink Antiequivalence_of_categories.
- Dieudonné_module wikiPageWikiLink Category:Algebraic_groups.
- Dieudonné_module wikiPageWikiLink Equivalence_of_categories.
- Dieudonné_module wikiPageWikiLink Field_(mathematics).
- Dieudonné_module wikiPageWikiLink Jean_Dieudonné.
- Dieudonné_module wikiPageWikiLink Mathematische_Annalen.
- Dieudonné_module wikiPageWikiLink Modularity_theorem.
- Dieudonné_module wikiPageWikiLink Module_(mathematics).
- Dieudonné_module wikiPageWikiLink Pierre_Cartier_(mathematician).
- Dieudonné_module wikiPageWikiLink Shimura–Taniyama_conjecture.
- Dieudonné_module wikiPageWikiLink Supersingular_elliptic_curve.
- Dieudonné_module wikiPageWikiLink Witt_vector.
- Dieudonné_module wikiPageWikiLink Witt_vectors.
- Dieudonné_module wikiPageWikiLinkText "Dieudonné module".
- Dieudonné_module authorlink "Jean Dieudonné".
- Dieudonné_module b "1".
- Dieudonné_module b "2".
- Dieudonné_module b "3".
- Dieudonné_module first "I.V.".
- Dieudonné_module hasPhotoCollection Dieudonné_module.
- Dieudonné_module id "D/d031640".
- Dieudonné_module last "Dieudonné".
- Dieudonné_module last "Dolgachev".
- Dieudonné_module p "p".
- Dieudonné_module wikiPageUsesTemplate Template:Citation.
- Dieudonné_module wikiPageUsesTemplate Template:Eom.
- Dieudonné_module wikiPageUsesTemplate Template:Harvs.
- Dieudonné_module wikiPageUsesTemplate Template:Su.
- Dieudonné_module year "1954".
- Dieudonné_module year "1957".
- Dieudonné_module subject Category:Algebraic_groups.
- Dieudonné_module comment "In mathematics, a Dieudonné module introduced by Dieudonné (1954, 1957b), is a module over the non-commutative Dieudonné ring, which is generated over the ring of Witt vectors by two special endomorphisms F and V called the Frobenius and Verschiebung operators.".
- Dieudonné_module label "Dieudonné module".
- Dieudonné_module sameAs m.0fp_ygg.
- Dieudonné_module sameAs Q5275225.
- Dieudonné_module sameAs Q5275225.
- Dieudonné_module wasDerivedFrom Dieudonné_module?oldid=575146780.
- Dieudonné_module isPrimaryTopicOf Dieudonné_module.