Local global principles for torsors under fundamental groups

点击翻译按钮获取中文摘要

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.