High Quality Content by WIKIPEDIA articles! 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 division points. For an abelian variety A defined over a field F with ring of integers R, consider the Neron model of A, which is a 'best possible' model of A defined over R. This model may be represented as a scheme over Spec(R) (cf. spectrum of a ring) for which the generic fibre constructed by means of the morphism Spec(F) ? Spec(R) gives back A.

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