Degenerating abelian varieties via log abelian varieties

2014/12/17 by Zhao, Heer
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14K99. Secondary 14D06

paper · doi:10.48550/arxiv.1412.5651

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.

Related

• Honda-Tate theory for log abelian varieties over finite fields
• Log p-divisible groups associated with semi-abelian degeneration
• Logarithmic good reduction of abelian varieties
• Logarithmic abelian varieties, Part VI: Local moduli and GAGF
• The log Grothendieck ring of varieties