Variétés abéliennes et ordres maximaux

  • Gaël Rémond

    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.

Cite this article

Gaël Rémond, Variétés abéliennes et ordres maximaux. Rev. Mat. Iberoam. 33 (2017), no. 4, pp. 1173–1195

DOI 10.4171/RMI/967