Proof of a conjecture of Colliot-Thélène and a diophantine excision theorem

Denef, Jan

doi:10.2140/ant.2019.13.1983

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Proof of a conjecture of Colliot-Thélène and a diophantine excision theorem

Jan Denef

Vol. 13 (2019), No. 9, 1983–1996

DOI: 10.2140/ant.2019.13.1983

Abstract

We prove a conjecture of Colliot-Thélène 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

Conjecture of Colliot-Thélène, Ax–Kochen Theorem, Diophantine equations, p-adic numbers, Forms in many variables, Diophantine geometry, Monomialization, Toroidalization of morphisms

Mathematical Subject Classification 2010

Primary: 14G20

Secondary: 11S05

Milestones

Received: 31 March 2016

Revised: 10 January 2019

Accepted: 14 May 2019

Published: 7 December 2019

Authors

Jan Denef
Department of Mathematics KULeuven Leuven Belgium

Vol. 13, No. 9, 2019