English

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.

Keywords

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

R2 v1 2026-06-21T16:55:25.397Z