Remarks on Non-Abelian Cohomology of Proalgebraic Groups

TL;DR

This paper discusses a variant of non-abelian cohomology for proalgebraic groups, extending Kim's work to analyze rational points on algebraic varieties over number fields.

Contribution

It introduces a new variant of non-abelian cohomology tailored for proalgebraic groups, applied to rational points of universal curves over moduli spaces.

Findings

Developed a detailed variant of non-abelian cohomology.

Applied the variant to study rational points on universal curves.

Extended Kim's framework to new algebraic contexts.

Abstract

These are detailed notes on a variant of the non-abelian cohomology developed by Minhyong Kim in arXiv:0409456 (published in Invent. Math.) to study rational points of varieties over number fields. The current variant is used in arXiv:1001.5008 to study rational points of the restriction of the universal curve to the generic point of M_{g,n}.