Vol. 13, No. 9, 2019

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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
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