Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type
Number Theory
2025-04-16 v1 Algebraic Geometry
Abstract
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-Th\'el\`ene-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.
Keywords
Cite
@article{arxiv.2302.11515,
title = {Brauer-Manin obstruction for Wehler K3 surfaces of Markoff type},
author = {Quang-Duc Dao},
journal= {arXiv preprint arXiv:2302.11515},
year = {2025}
}
Comments
38 pages; comments are welcome. arXiv admin note: text overlap with arXiv:2202.07142