Families of trianguline representations, finite slope spaces and eigenvarieties

三角线表示族、有限斜率空间和特征簇

• 批准号: 221576595
• 负责人: Professor Dr. Eugen Hellmann
• 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: 2012
• 资助国家: 德国
• 起止时间: 2011-12-31 至 2012-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/221576595?language=en
• 关键词: Families; trianguline; representations; finite; slope

This project lies on the crossroads between Algebraic Geometry, Algebraic Number theory and the theory of automorphic forms. I want to study families of p-adic representations of p-adic Galois groups, and, more precisely, the class of so called trianguline representations. This study should yield on the one hand a new approach to Kisins finite slope space, on the other hand it should generalize this construction. Then I want to compare the resulting spaces with eigenvarieties, i.e with spaces parametrizing p-adic families of automorphic forms. Further I will discuss the connection with the Langlands program and the Fontaine-Mazur conjecture, i.e. with the conjectural connection between Galois representations and automorphic forms.

这个项目位于代数几何，代数数论和自守形式理论之间的十字路口。我想研究p-adic伽罗瓦群的p-adic表示族，更确切地说，是所谓的三角线表示类。本文的研究一方面为Kisins有限斜率空间提供了一种新的方法，另一方面也推广了这一构造。然后，我想比较所得的空间与本征簇，即与参数化自守形式的p-adic族的空间。此外，我将讨论与朗兰兹计划和Fontaine-Mazur猜想的联系，即与伽罗瓦表示和自守形式之间的几何联系。