Failure of strong approximation on an affine cone
Martin Bright, Ivo Kok
TL;DR
This paper investigates why strong approximation fails on certain affine cones by using the Brauer-Manin obstruction to explain the behavior of coprime integer solutions to homogeneous Diophantine equations.
Contribution
It introduces a novel application of the Brauer-Manin obstruction to understand the failure of strong approximation on affine cones.
Findings
Brauer-Manin obstruction explains failure of strong approximation
Coprime solutions exhibit specific obstructions
Provides new insights into Diophantine equations and rational points
Abstract
We use the Brauer-Manin obstruction to strong approximation on a punctured affine cone to explain a curious property of coprime integer solutions to a homogeneous Diophantine equation.
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