Obstruction sets and extensions of groups (Q2809367)

The main object of the paper under review is a smooth, projective, geometrically integral variety \(X\) defined over a number field \(k\). The author is interested in comparing various obstructions to the Hasse principle and weak approximation. She subdivides all known obstructions into two big classes: those related to the Brauer group of \(X\) and to descent on torsors under a linear algebraic group \(G\). One of her goals is to reconcile the Brauer-type and descent-type languages used to describe the obstructions. Towards this end, she gives an overview of the known results relating these two types of obstructions and also presents some new ones. In particular, such comparison theorems are proved for the case where \(G\) is unipotent or solvable. At the end, she produces a nice diagram showing all known interrelations between different types of obstructions.