Descent theory for open varieties
Algebraic Geometry
2010-12-09 v1 Number Theory
Abstract
We extend the descent theory of Colliot-Th\'el\`ene 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.
Cite
@article{arxiv.1012.1765,
title = {Descent theory for open varieties},
author = {David Harari and Alexei N. Skorobogatov},
journal= {arXiv preprint arXiv:1012.1765},
year = {2010}
}
Comments
28 pages