Vol. 12, No. 2, 2019

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

Volume 12
Issue 2, 181–360
Issue 1, 1–180

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Failure of strong approximation on an affine cone

Martin Bright and Ivo Kok

Vol. 12 (2019), No. 2, 321–327
DOI: 10.2140/involve.2019.12.321
Abstract

We use the Brauer–Manin obstruction to strong approximation on a punctured affine cone to explain why some mod p solutions to a homogeneous Diophantine equation of degree 2 cannot be lifted to coprime integer solutions.

Keywords
Brauer–Manin obstruction, integral points, strong approximation
Mathematical Subject Classification 2010
Primary: 11G35
Secondary: 14G25, 14F22, 11D09
Milestones
Received: 27 November 2017
Revised: 29 January 2018
Accepted: 13 March 2018
Published: 8 October 2018

Communicated by Bjorn Poonen
Authors
Martin Bright
Mathematisch Instituut
Universiteit Leiden
Leiden
Netherlands
Ivo Kok
Mathematisch Instituut
Universiteit Leiden
Leiden
Netherlands