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arXiv · 2209.15582

Semi-integral Brauer-Manin obstruction and quadric orbifold pairs

Vladimir Mitankin·Masahiro Nakahara·Sam Streeter
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Abstract

We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer-Manin obstruction interpolating between Manin's classical version for rational points and the integral version developed by Colliot-Th\'el\`ene and Xu. We determine the status of local-global principles, and obstructions to them, in two families of orbifolds naturally associated to quadric hypersurfaces. Further, we establish a quantitative result measuring the failure of the semi-integral Brauer-Manin obstruction to account for its integral counterpart for affine quadrics.

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Vladimir Mitankin, Masahiro Nakahara, Sam Streeter. 2022-09-30. Semi-integral Brauer-Manin obstruction and quadric orbifold pairs. https://doi.org/10.1090/tran%2F9170

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