Conductor of an abelian variety

In mathematics, in Diophantine geometry, the conductor of an abelian variety defined over a local or global field F is a measure of how "bad" the bad reduction at some prime is.

It is connected to the ramification in the field generated by the torsion points.

spectrum of a ring) for which the generic fibre constructed by means of the morphism gives back A.

Let A0 denote the open subgroup scheme of the Néron model whose fibres are the connected components.

For a maximal ideal P of R with residue field k, A0k is a group variety over k, hence an extension of an abelian variety by a linear group.