Rational Points and Arithmetic of Fundamental Groups: Evidence for the Section Conjecture

The first exposition of foundational material on the arithmetic of fundamental groups with respect to the Section Conjecture of anabelian Geometry: from the history of the subject to the state of the art of the conjecture. Numerous approaches to the Section Conjecture are discussed with open questions to stimulate future research. Assuming the basics, the more advanced chapters are self contained and can be read independently Includes supplementary material: sn.pub/extras