主极化阿贝尔簇的唯一分解
代数几何
2016-07-18 v2 数论
摘要
Shimura证明了 上的每个主极化阿贝尔簇都容许唯一分解为不可约主极化阿贝尔簇。我们阐述他的结果，并将其推广到任意基域 。若 是可分闭的，则不可约因子与产生该极化的theta除子的不可约分支一一对应。
引用
@article{arxiv.1602.06811,
title = {Unique factorization of principally polarized abelian varieties},
author = {Bruce W. Jordan and Allan G. Keeton and Bjorn Poonen},
journal= {arXiv preprint arXiv:1602.06811},
year = {2016}
}
备注
The paper "Polarisations sur les vari\'{e}t\'{e}s ab\'{e}liennes produits" (C. R. Acad. Sci. Paris, t. 323, S\'{e}rie 1, p. 631-635, 1996) by Olivier Debarre, of which we were initially unaware, contains stronger results than ours