Integral Hasse principle and strong approximation for Markoff surfaces
Daniel Loughran, Vladimir Mitankin
TL;DR
This paper investigates why certain Markoff surfaces fail to satisfy the integral Hasse principle and strong approximation, focusing on the role of the Brauer-Manin obstruction in these failures.
Contribution
It provides a detailed analysis of the failure mechanisms for the integral Hasse principle and strong approximation on Markoff surfaces, extending previous work with new insights.
Findings
Identification of Brauer-Manin obstruction as a key factor
Examples of Markoff surfaces failing the integral Hasse principle
Conditions under which strong approximation fails
Abstract
We study the failure of the integral Hasse principle and strong approximation for Markoff surfaces, as studied by Ghosh and Sarnak, using the Brauer-Manin obstruction.
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