Vol. 12, No. 2, 2019

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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.

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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