Semi-integral Brauer-Manin obstruction and quadric orbifold pairs

verfasst von

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-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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

Bulgarian Academy of Sciences (BAS)
University of Washington (UW)
University of Bristol

Typ

Artikel

Journal

Transactions of the American Mathematical Society

Band

377

Seiten

4435-4480

Anzahl der Seiten

46

ISSN

0002-9947

Publikationsdatum

06.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Allgemeine Mathematik, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1090/tran/9170 (Zugang: Geschlossen)
https://doi.org/10.48550/arXiv.2209.15582 (Zugang: Offen)