About: Semistable abelian variety

In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces at the primes of the field. For an abelian variety defined over a field with ring of integers , consider the Néron model of , which is a 'best possible' model of defined over . This model may be represented as a scheme over (cf. spectrum of a ring) for which the generic fibre constructed by means of the morphismgives back . The Néron model is a smooth group scheme, so we can consider , the connected component of the Néron model which contains the identity for the group law. This is an open subgroup scheme of the Néron model. For a residue field , is a group variety over , hence an extension of an abelian variety by a linear group. If