Toroidal Resolutions for Some Matrix Singularities
Toroidal Resolutions for Some Matrix Singularities
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某些矩阵奇点的环形分辨率
DOI：
10.1007/978-3-0348-8303-0_5
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发表时间：
2001
影响因子：
0.9
通讯作者：
G. Faltings
中科院分区：
文献类型：
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作者：
G. Faltings
在具有层结构的阿贝尔簇的模曲线经典理论中，德林费尔德层结构起着重要作用。这些结构使我们能够在坏特征的素数上找到相当好的模型，例如可参见卡茨（Katz）和马祖尔（Mazur）所著的[KM]一书。不幸的是，对于更高维度的阿贝尔簇，我们没有这样的工具。作为一种适度的替代方法，可以使用相关奇点的显式方程。这些方程由矩阵之间的恒等式给出，但它们仅涵盖层可被特征\(p\)整除但不被\(p^{2}\)整除的情况。在这方面，柴（Chai）/诺曼（Norman）以及德利涅（Deligne）/帕帕斯（Pappas）是先驱者（[CN]，[DP]）。在之前的一篇论文[F]中，我已经为与对称空间相关的此类奇点构建了显式消解。在此，我们（在某些情况下）将此扩展到与一个伊瓦霍里（Iwahori）子群相关的层结构，这似乎是通过这些方法可达到的最大可能。然而，我们只能证明我们的模型具有环面奇点。
In the classical theory of modular curves parametrising abelian varieties with level structures an important role is played by Drinfeld level structures. These allow us to find reasonably good models over primes of bad characteristics, see for example the book [KM] by Katz and Mazur. Unfortunately we have no such device for abelian varieties of higher dimensions. As a modest replacement one can use explicit equations for the relevant singularities. These are given by identities between matrices, but they cover only the case where the level is divisible by the characteristicpbut not by its square. Here the pioneers are Chai/Norman and Deligne/Pappas ([CN], [DP]). In a previous paper [F] I had constructed explicit resolutions for such singularities which are associated to symmetric spaces. Here we extend this (in some cases) to the level structures associated to an Iwahori subgroup, which seems to be the maximum possible accessible by these methods. However we can only show that our models have toroidal singularities.