Semistable resolutions of local models

局部模型的半稳定分辨率

• 批准号: 239457008
• 负责人: Professor Dr. Ulrich Görtz
• 金额: --
• 依托单位: Institut für Experimentelle Mathematik (IEM)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/239457008?language=en
• 关键词: Semistable; resolutions; local; models

The goal of this project is the investigation of a topic in arithmetic algebraic geometry by algorithmic and experimental methods. Local models describe the étale-local structure of integral models of certain Shimura varieties, and therefore, as well as for other reasons, are of great interest in arithmetic geometry. However, in general their singularities are so complicated that it would be desirable to pass to a model with less severe singularities, in the best case to a semistable model. In general it is not known whether such a model exists. This is what we will investigate by explicit computations. In cases of “small rank” computations (by the principal investigator, among others) have shown that a semistable resolution exists. In the general case there are candidates for semistable resolutions, for example by Genestier and Faltings, but so far (without using computers) their semistability could not be proved. In addition, this and similar questions can also be investigated for other classes of schemes, for instance for certain degenerations of quiver Grassmannians.

这个项目的目标是用算法和实验的方法来研究算术代数几何中的一个主题。局部模型描述了某些志村类型的积分模型的<s:1> -局部结构，因此，以及其他原因，在算术几何中引起了极大的兴趣。然而，一般来说，它们的奇点是如此复杂，以至于最好将其传递给具有不太严重奇点的模型，在最好的情况下传递给半稳定模型。一般来说，这种模式是否存在是未知的。这就是我们将通过显式计算来研究的。在“小秩”计算的情况下（由主要研究者和其他人）已经表明存在半稳定分辨率。在一般情况下，有半稳定分辨率的候选，例如Genestier和Faltings，但到目前为止（没有使用计算机）它们的半稳定性无法证明。此外，这个问题和类似的问题也可以研究其他类型的方案，例如颤栗格拉斯曼的某些退化。