Vol. 13, No. 9, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 1681–1865
Issue 9, 1533–1680
Issue 8, 1359–1532
Issue 7, 1239–1357
Issue 6, 1127–1237
Issue 5, 981–1126
Issue 4, 805–980
Issue 3, 541–804
Issue 2, 267–539
Issue 1, 1–266

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
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