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Semi-integral Brauer--Manin obstruction and quadric orbifold pairs.

Authors :
Mitankin, Vladimir
Nakahara, Masahiro
Streeter, Sam
Source :
Transactions of the American Mathematical Society. Jun2024, Vol. 377 Issue 6, p4435-4480. 46p.
Publication Year :
2024

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. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00029947
Volume :
377
Issue :
6
Database :
Academic Search Index
Journal :
Transactions of the American Mathematical Society
Publication Type :
Academic Journal
Accession number :
177372859
Full Text :
https://doi.org/10.1090/tran/9170