English

Proof of a conjecture of Colliot-Th\'el\`ene

Algebraic Geometry 2019-12-11 v2 Number Theory

Abstract

We prove a conjecture of Colliot-Th\'el\`ene that implies the Ax-Kochen Theorem on p-adic forms. We obtain it as an easy consequence of a diophantine excision theorem whose proof forms the body of the present paper.

Keywords

Cite

@article{arxiv.1108.6250,
  title  = {Proof of a conjecture of Colliot-Th\'el\`ene},
  author = {Jan Denef},
  journal= {arXiv preprint arXiv:1108.6250},
  year   = {2019}
}

Comments

18 pages. Substantial revision to improve the exposition. A few mistakes corrected. The Diophantine Purity Theorem is now called the Diophantine Excision Theorem