Local global principles for torsors under fundamental groups

基本组下 Torsors 的局部全局原则

• 批准号: 2071872
• 金额: --
• 依托单位: UNIVERSITY OF EXETER
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2071872
• 关键词: Local; global; principles; torsors; under

A much important principle in number theory and arithmetic geometry is the local global principle, especially the local global principle for rational points of algebraic varieties and more generally the local global principle for torsors under various groups. Given various mathematical objects and structures defined over number fields one aims to relate properties of these structures to those of the same structure but viewed over the various localisations of the number field; the so-called local fields. The research project of Christopher Haines aims to establish new local global principles for certain non abelian Galois cohomology groups with coefficients which are non abelian fundamental groups of curves over number fields. Such a local global principle is known for torsors under pro-solvable fundamental groups of hyperbolic curves over number fields. The main objective of this project is to establish a similar principle for pro-solvable fundamental groups of affine curves over number fields.

数论和算术几何中一个非常重要的原理是局部整体原理，特别是代数簇的有理点的局部整体原理，更一般的是各种群下的扭体的局部整体原理。给定定义在数域上的各种数学对象和结构，我们的目标是将这些结构的性质与相同结构的性质联系起来，但要从数域的各种局部化（即所谓的局部域）来看待。 Christopher Haines的研究项目旨在为某些系数为数域上曲线的非交换基本群的非交换Galois上同调群建立新的局部整体原理。这样的局部整体原理是已知的torsors pro-solvable基本群的双曲曲线在数域上。本项目的主要目标是建立数域上仿射曲线的准可解基本群的相似原理。