We show that any abelian variety that is not affine has a nontrivial strongly abelian subvariety. In later papers in this sequence, we apply this result to the study of minimal abelian varieties.

中文翻译：

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代数的最小阿贝尔簇，I

我们证明任何非仿射的阿贝尔变体都具有非平凡的强阿贝尔子变体。在此序列的后续论文中，我们将此结果应用于最小阿贝尔簇的研究。