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arXiv · 2010.07995

Abelian varieties, quaternion trick and endomorphisms

Yuri G. Zarhin
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Abstract

Let $X$ be a polarized abelian variety over a field $K$. Let $O$ be a ring with an involution that acts on $X$ and this action is compatible with the polarization. We prove that the natural action of $O$ on $(X \times X^t)^4$ is compatible with a certain principal polarization.

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Yuri G. Zarhin. 2020-10-15. Abelian varieties, quaternion trick and endomorphisms. https://arxiv.org/abs/2010.07995

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