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-Thélène 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.
Original language | English |
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Pages (from-to) | 4435-4480 |
Number of pages | 46 |
Journal | Transactions of the American Mathematical Society |
Volume | 377 |
Issue number | 6 |
Early online date | 19 Apr 2024 |
DOIs | |
Publication status | E-pub ahead of print - 19 Apr 2024 |