Degenerating abelian varieties via log abelian varieties

TL;DR

This paper constructs log abelian varieties extending split totally degenerate abelian varieties over discrete valuation fields, generalizing Kato's log Tate curve, thus advancing the understanding of degenerations in algebraic geometry.

Contribution

It introduces a method to extend split totally degenerate abelian varieties to log abelian varieties over valuation rings, broadening the scope of log geometric techniques.

Findings

Construction of log abelian varieties over valuation rings

Extension of split totally degenerate abelian varieties

Generalization of the log Tate curve

Abstract

For any split totally degenerate abelian variety over a complete discrete valuation field, we construct a log abelian variety over the discrete valuation ring extending the given abelian variety. This generalizes the log Tate curve of Kato.