Geometrically simple quasi-abelian varieties

Yukitaka Abe

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arXiv · 1706.10032

Geometrically simple quasi-abelian varieties

Yukitaka Abe

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Abstract

We define the geometric simpleness for toroidal groups. We give an example of quasi-abelian variety which is geometrically simple, but not simple. We show that any quasi-abelian variety is isogenous to a product of geometrically simple quasi-abelian varieties. We also show that the ${\mathbb Q}$-extension of the ring of all endomorphisms of a geometrically simple quasi-abelian variety is a division algebra over ${\mathbb Q}$.

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BibTeX RIS

Yukitaka Abe. 2017-11-27. Geometrically simple quasi-abelian varieties. https://arxiv.org/abs/1706.10032

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