Integral Hasse principle and strong approximation for Markoff surfaces

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.

28 pages

References in corpus (8)

• Brauer-Manin obstruction for integral points of homogeneous spaces and representation by integral quadratic forms
• Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines
• Failures of weak approximation in families
• Integral points on Markoff type cubic surfaces
• Rational points of bounded height on general conic bundle surfaces
• Obstructions to the Hasse principle in families
• Brauer-Manin obstruction for Markoff surfaces
• A uniform bound on the Brauer groups of certain log K3 surfaces

Cited by in corpus (7)

• Integral points on Markoff type cubic surfaces
• Brauer-Manin obstruction for Markoff surfaces
• Rational points on del Pezzo surfaces of degree four
• Commutators in ${\mathrm{SL}}_2$ and Markoff surfaces I
• Brauer-Manin obstruction for integral points on Markoff-type cubic surfaces
• Semi-integral Brauer-Manin obstruction and quadric orbifold pairs
• Brauer-Manin obstruction for Erdős-Straus surfaces