Semistable reduction and torsion subgroups of abelian varieties
Alice Silverberg, Yuri Gennad'evich Zarhin · Annales de l’institut Fourier · 1995
The main result of this paper implies that if an abelian variety over a field F has a maximal isotropic subgroup of n -torsion points all of which are defined over F , and n ≥ 5 , then the abelian variety has semistable reduction away from n . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its n -torsion points are defined over a field F and n ≥ 3 , then the abelian variety has semistable reduction away from n . We also give information about the Néron models in the cases where n = 2 , 3 and 4.