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arXiv · 1602.06811

Unique factorization of principally polarized abelian varieties

Bruce W. Jordan·Allan G. Keeton·Bjorn Poonen
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Abstract

Shimura proved that each principally polarized abelian variety over $\mathbf{C}$ admits a unique factorization into irreducible principally polarized abelian varieties. We give an exposition of his result, and generalize to an arbitrary ground field $k$. If $k$ is separably closed, the irreducible factors are in bijection with the irreducible components of a theta divisor over $k$ giving rise to the polarization.

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Bruce W. Jordan, Allan G. Keeton, Bjorn Poonen. 2016-07-15. Unique factorization of principally polarized abelian varieties. https://arxiv.org/abs/1602.06811

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