Log $p$-divisible groups associated with semi-abelian degeneration

TL;DR

This paper studies how torsion point group schemes of abelian schemes degenerate into log finite group schemes during semi-abelian degeneration along normal crossings, revealing richer information than traditional approaches.

Contribution

It introduces a framework for understanding the degeneration of torsion point group schemes into log finite group schemes in semi-abelian degenerations.

Findings

Degeneration of torsion point group schemes into log finite group schemes.

Log finite group schemes capture more information than quasi-finite flat group schemes.

Applicable to semi-abelian degenerations along normal crossings.

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.