Affine Deligne-Lusztig theory

仿射德利涅-鲁斯蒂格理论

• 批准号: 318872759
• 负责人: Professor Dr. Alexander Ivanov
• 金额: --
• 依托单位: Institut de Mathématiques de Jussieu-Paris Rive Gauche (UMR 7586)
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/318872759?language=en
• 关键词: Affine; Deligne; Lusztig; theory

The classical Deligne-Lusztig theory gives a complete description of representations of connected reductive groups over finite fields in terms of algebraic geometry. The goal of this project is to develop a complete analog of the classical Deligne-Lusztig theory for connected reductive groups over local fields. This should contribute to the automorphic induction and a purely local geometric proof of the local Langlands correspondence. Especially in the ramified case this leads to substantially new insights. A purely local proof of the local Langlands correspondence is very desirable: it has the same importance for the contemporary arithmetic geometry as the purely local approach to the local class field theory had for the algebraic number theory in the 1930s.

经典的delig - lusztig理论给出了有限域上连通约化群的代数几何表示的完整描述。本项目的目标是为局部域上的连通约化群建立一个完全类似于经典delig - lusztig理论的模型。这将有助于自同构归纳和局部朗兰兹对应的纯粹局部几何证明。特别是在分支的情况下，这导致了实质性的新见解。局部朗兰兹对应的纯局部证明是非常可取的：它对当代算术几何的重要性，就像局部类场论的纯局部方法对20世纪30年代代数数论的重要性一样。

项目成果

Affine Deligne–Lusztig varieties at infinite level

Affine Deligneâ无限层次的甘美品种

• DOI: 10.1007/s00208-020-02092-4
• 发表时间: 2021
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: Charlotte;Ivanov;Alexander
• 通讯作者: Alexander