Semi-integral Brauer–Manin obstruction and quadric orbifold pairs

V. Mitankin, M. Nakahara, S. Streeter

Research output: Contribution to journalArticle (Academic Journal)peer-review

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 languageEnglish
Pages (from-to)4435-4480
Number of pages46
JournalTransactions of the American Mathematical Society
Volume377
Issue number6
Early online date19 Apr 2024
DOIs
Publication statusE-pub ahead of print - 19 Apr 2024

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