A global study of the moduli spaces of abelian varieties over the ring of integers

在阿贝尔变模理论中，我们证明了以下结论：定理：存在另一个正则紧化SQ^<环>_<g,k>不同于我们在1999年构造的SQ_<g,k>。此外，还存在从SQ_<环>_<g,k>到SQ_<g,k>的正则双射国家态射，从而导出了它们的归一化的同构性。在强化二维麦凯对应关系方面也取得了进展，这解释了与扩展的Dynkin图的联系。

We proved the following in the theory of moduli of abelian varieties :Theorem : There is another canonical compactification SQ^<toric>_<g,k> of the moduli of abelian varieties different from SQ_<g,k> constructed by us in 1999. Moreover there is a canonical bijectivebirationalmorphism from SQ^<toric>_<g,k> onto SQ_<g,k> which induces the isomorphism of their normalizations.There was also a progress in sharpening the 2-dimensional McKay correspondence, which explains the connection with the extended Dynkin diagram.