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arXiv · 2504.10992

Rational and integral points on Markoff-type K3 surfaces

Quang-Duc Dao
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Abstract

Following recent works by E. Fuchs et al. and by the author, we study rational and integral points on Markoff-type K3 (MK3) surfaces, i.e., Wehler K3 surfaces of Markoff type. In particular, we construct a family of MK3 surfaces which have a Zariski dense set of rational points but fail the integral Hasse principle due to the Brauer-Manin obstruction and provide some counting results for this family. We also give some remarks on Brauer groups, Picard groups, and failure of strong approximation on MK3 surfaces.

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Quang-Duc Dao. 2025-04-15. Rational and integral points on Markoff-type K3 surfaces. https://arxiv.org/abs/2504.10992

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