Purity of stable pieces in compactifications of semisimple groups

半单群紧化中稳定片的纯度

• 批准号: 124649447
• 负责人: Professor Dr. Torsten Wedhorn
• 金额: --
• 依托单位: Arbeitsgruppe Algebra
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2009
• 资助国家: 德国
• 起止时间: 2008-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/124649447?language=en
• 关键词: Purity; stable; pieces; compactifications; semisimple

One of the most fruitful techniques to understand geometric objects is to attach to them linear invariants. The study of these invariants often leads to a problem within representation theory. One important question for these invariants is whether they have the property to be pure. A positive answer allows to control the degeneration of geometric objects. An important linear invariant is the De Rham cohomology. For certain geometric objects playing a central role in number theory (e.g., abelian varieties, curves, or p-divisible groups in positive characteristic) their De Rham cohomology carries the structure of a so-called truncated crystal. These can be considered in two ways as objects within the area of representation theory: as representation of certain clans in the sense of Crawley-Boevey or as stable pieces in a compactification of the projective linear group. The goal of this project is to study whether the De Rham cohomology is pure focussing on the second interpretation.

理解几何对象最富有成效的技术之一是为它们附加线性不变量。对这些不变量的研究经常会导致表示论中的一个问题。这些不变量的一个重要问题是它们是否具有纯的性质。一个肯定的答案允许控制几何对象的退化。一个重要的线性不变量是De Rham上同调。对于某些在数论中起核心作用的几何对象（例如，阿贝尔簇、曲线或正特征的p-可分群），它们的De Rham上同调具有所谓的截断晶体的结构。这些可以在两个方面被认为是表示论领域内的对象：作为克劳利-博维意义上的某些氏族的表示，或者作为射影线性群的紧化中的稳定块。这个项目的目标是研究De Rham上同调是否是纯粹的，重点是第二种解释。