Revista Matemática Iberoamericana

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Volume 33, Issue 4, 2017, pp. 1173–1195
DOI: 10.4171/RMI/967

Published online: 2017-11-17

Variétés abéliennes et ordres maximaux

Gaël Rémond[1]

(1) Université Grenoble Alpes, Grenoble, France

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.

Keywords: Variété abélienne, endomorphisme, ordre, ordre maximal

Rémond Gaël: Variétés abéliennes et ordres maximaux. Rev. Mat. Iberoamericana 33 (2017), 1173-1195. doi: 10.4171/RMI/967