Reduction of abelian varieties

1996/02/19 by Silverberg, A., Zarhin, Yu. G.
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9602014

Abstract

We study semistable reduction and torsion points of abelian varieties. In particular, we give necessary and sufficient conditions for an abelian variety to have semistable reduction. We also study Néron models of abelian varieties with potentially good reduction and torsion points of small order. We study some invariants that measure the extent to which an abelian variety with potentially good reduction fails to have good reduction.

Related

• Semistable reduction of abelian varieties over extensions of small degree
• Semistable abelian varieties over ℚ with bad reduction at 19 only
• Purely additive reduction of abelian varieties with torsion
• Non-existence of certain semistable abelian varieties
• Abelian varieties over Q with bad reduction in one prime only