The classification of p-divisible groups over 2-adic discrete valuation rings

2010/07/12 by Wausu Kim, Kim, Wausu
Mathematics · #11S20 #14F30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Business #Compatibility (geochemistry) #Discrete mathematics #Discrete valuation #Discrete valuation ring #FOS: Mathematics #Field (mathematics) #Mathematics #Number Theory (math.NT) #Pure mathematics #Residue field #Valuation (finance) #Valuation ring #math.AG #math.NT #msc:11S20 #msc:14F30

paper · pdf · doi:10.48550/arxiv.1007.1904

Final Version (with improved proofs and some re-ordering of sections). To appear in Math. Res. Lett

openalex publication_date 2010/07/12 · arxiv created 2011/12/30 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \mathscrO_K be a 2-adic discrete valuation ring with perfect residue field k. We classify p-divisible groups and p-power order finite flat group schemes over \mathscrO_K in terms of certain Frobenius module over \mathfrakS:=W(k)[[u]]. We also show the compatibility with crystalline Dieudonné theory and associated Galois representations. Our approach differs from Lau's generalization of display theory, and we additionally obtain the the compatibility with associated Galois representations.

Related

• The relative Breuil-Kisin classification of p-divisible groups and finite flat group schemes
• Smoothness of the truncated display functor
• Group schemes of period p>2
• Integral p-adic Hodge theory in the imperfect residue field case
• Divided Dieudonné crystals