Abelian varieties and maximal orders
type: Item
instance of: scholarly article
title: Abelian varieties and maximal orders
zbMATH Open document ID: 1441.11157
DOI: 10.4171/RMI/967
author: Gaël Rémond
published in: Revista Matemática Iberoamericana
publication date: 2018-01-04T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 14K05
Mathematics Subject Classification ID: 16H10
zbMATH DE Number: 6821827
zbMATH Keywords: abelian variety
zbMATH Keywords: endomorphism
zbMATH Keywords: order
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rmi/967
OpenAlex ID: W2770268572
description: scientific article; zbMATH DE number 6821827