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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 Néron 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.