Semi-integral Brauer-Manin obstruction and quadric orbifold pairs

authored by

Vladimir Mitankin, Masahiro Nakahara, Sam Streeter

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

Type

Preprint

Publication date

30.09.2022

Publication status

Published