Crystalline Dieudonné module theory via formal and rigid geometry
type: Item
instance of: scholarly article
title: Crystalline Dieudonné module theory via formal and rigid geometry
zbMATH Open document ID: 0864.14009
DOI: 10.1007/BF02698637
published in: Publications Mathématiques
publication date: 1996-09-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104109
review text: Dieudonné theory associates to a \(p\)-adic divisible group a Dieudonné-crystal, that is (roughly) a module with connection, fibration and Frobenius. The idea is that these are easier to handle than \(p\)-divisible groups. Except for some minor technical restrictions the paper shows that over a field \(R\) of characteristic \(p\) the functor is an equivalence of categories for smooth formal schemes, and still fully faithful up to isogeny for arbitrary reduced schemes. For the first result the author first treats fields, then studies deformations, and finally uses noetherian induction. For this last step one is already forced to work in the additional generality of formal schemes. The proof of the second result is very complicated and uses rigid-analytic methods.
Mathematics Subject Classification ID: 14F30
Mathematics Subject Classification ID: 14L05
Mathematics Subject Classification ID: 18F20
zbMATH DE Number: 910524
zbMATH Keywords: \(p\)-adic divisible group
zbMATH Keywords: Dieudonné-crystal
zbMATH Keywords: formal schemes
author: Aise Johan de Jong
MaRDI profile type: Publication
cites work: Cohomologie cristalline des schemas de caractéristique \(p >0\)
cites work: Q3661717
cites work: Q3325851
cites work: Formal and rigid geometry. I: Rigid spaces
cites work: Complete Intersections and Connectedness
cites work: Complexe cotangent et déformations. I. (The cotangent complex and deformations. I.)
cites work: Q5190295
cites work: Complexe de de\thinspace Rham-Witt et cohomologie cristalline
cites work: Finite locally free group schemes in characteristic \(p\) and Dieudonné modules
cites work: Étale cohomology of rigid analytic spaces
cites work: Der Satz von Remmert-Stein in der nichtarchimedischen Funktionentheorie
cites work: Fortsetzbarkeit \(k\)-meromorpher Funktionen
cites work: Q3882554
cites work: Universal extensions and one dimensional crystalline cohomology
cites work: The crystals associated to Barsotti-Tate groups: with applications to Abelian schemes
OpenAlex ID: W2151463592
reviewed by: Gerd Faltings
description: scientific article; zbMATH DE number 910524