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Abelian varieties and maximal orders. (Variétés abéliennes et ordres maximaux.) (French. English summary) Zbl 1441.11157

Summary: We prove that an abelian variety whose endomorphism ring is a maximal order can be written as a direct product of simple factors with the same property, in which furthermore two isogenous factors have isomorphic nth powers for some n. Conversely every such product has a maximal order as endomorphism ring. We deduce from this some properties for arbitrary abelian varieties, in particular for almost complements of abelian subvarieties.

MSC:

11G10 Abelian varieties of dimension \(> 1\)
14K05 Algebraic theory of abelian varieties
16H10 Orders in separable algebras
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