Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type

Following recent work by E. Fuchs et al., we study the Brauer-Manin obstruction for integral points on Wehler K3 surfaces of Markoff type. In particular, we construct some families which fail the integral Hasse principle via the Brauer-Manin obstruction with some counting results of similar nature t...

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Published in:arXiv.org 2023-02
Main Author: Quang-Duc Dao
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description Following recent work by E. Fuchs et al., we study the Brauer-Manin obstruction for integral points on Wehler K3 surfaces of Markoff type. In particular, we construct some families which fail the integral Hasse principle via the Brauer-Manin obstruction with some counting results of similar nature to those in previous works by Ghosh-Sarnak, Loughran-Mitankin, Colliot-Thélène-Wei-Xu. We also give some counterexamples to strong approximation (where integral points can exist) which can be explained by the Brauer-Manin obstruction, and study a few aspects of rational points on affine surfaces.
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title Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type
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