paper

Descent theory for open varieties

arXiv:1012.1765

Abstract

We extend the descent theory of Colliot-Thélène and Sansuc to arbitrary smooth algebraic varieties by removing the condition that every invertible regular function is constant. This links the Brauer--Manin obstruction for integral points on arithmetic schemes to the obstructions defined by torsors under groups of multiplicative type.

28 pages

Descent theory for open varieties · wovepaper