Log p-divisible groups associated with semi-abelian degeneration

2025/05/06 by Inoue, Kentaro
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.03993

Abstract

In this paper, we prove that, when an abelian scheme has semi-abelian degeneration along normal crossings divisor in a regular base scheme, a finite flat group scheme of torsion points of the abelian scheme degenerates to a log finite group scheme, which captures more information than a quasi-finite flat group scheme of torsion points of the semi-abelian scheme.

Citations

• Log Prismatic Dieudonné theory and its application to Shimura varieties
• Slope filtrations of log p-divisible groups
• Log p-divisible groups and semi-stable representations
• Moduli of logarithmic abelian varieties with PEL structure
• Logarithmic abelian varieties, Part VII: Moduli
• Logarithmic structures of Fontaine-Illusie. II
• Logarithmic abelian varieties, Part VI: Local moduli and GAGF
• Toroidal compactifications of integral models of Shimura varieties of\n Hodge type
• Théorie de Hodge : III

Related

• Abelian Log Fundamental Group scheme
• Degenerating abelian varieties via log abelian varieties
• Comparison of Kummer logarithmic topologies with classical topologies II
• The higher direct images of locally constant group schemes from the Kummer log flat topology to the classical flat topology
• Logarithmic Dieudonne theory