Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic

DOI10.1016/j.jnt.2012.03.010zbMath1283.11091arXiv0911.2474OpenAlexW2093062747MaRDI QIDQ432471

Adrian Vasiu, Thomas Zink

Publication date: 4 July 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.2474

zbMATH Keywords

group schemes\(p\)-divisible groupsBreuil modulesdiscrete valuation ringstruncated Barsotti-Tate groups

Mathematics Subject Classification ID

Galois cohomology (11S25) Abelian varieties of dimension (> 1) (11G10) Arithmetic aspects of modular and Shimura varieties (11G18) Group schemes (14L15)

Related Items

Breuil 𝒪-windows and 𝜋-divisible 𝒪-modules, On the u^∞-torsion submodule of prismatic cohomology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Relations between Dieudonné displays and crystalline Dieudonné theory
• Frames and finite group schemes over complete regular local rings
• Purity results for \(p\)-divisible groups and Abelian schemes over regular bases of mixed characteristic
• Modularity of 2-adic Barsotti-Tate representations
• The classification of \(p\)-divisible groups over 2-adic discrete valuation rings
• The correspondence between Barsotti-Tate groups and Kisin modules when \(p=2\)
• Potentially good reduction of Barsotti-Tate groups
• Breuil's classification of $p$-divisible groups over regular local rings of arbitrary dimension
• Crystalline boundedness principle
• Schémas en groupes de type $(p,\ldots,p)$
• Torsion p-adic Galois representations and a conjecture of Fontaine
• Crystalline representations and F-crystals
• The generic fibre of finite group schemes; a “finite wild” criterion for good reduction of Abelian varieties