Semi-integral Brauer–Manin obstruction and quadric orbifold pairs

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-04-19 DOI:10.1090/tran/9170

Vladimir Mitankin, Masahiro Nakahara, Sam Streeter

引用次数: 0

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.

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半积分布劳尔-马宁阻塞和四面轨道对

我们研究了两个半积分点概念的局部-全局原理，这两个概念分别称为坎帕纳点和达蒙点。特别是，我们在马宁关于有理点的经典版本与科利奥-泰莱（Colliot-Thélène）和徐（Xu）开发的积分版本之间，开发了半积分版本的布劳尔-马宁阻碍（Brauer-Manin obstruction）。我们确定了局部-全局原理的地位，以及它们在与二次曲超曲面天然相关的两个轨道系中的阻碍作用。此外，我们还建立了一个定量结果，衡量半积分布劳尔-马宁阻碍是否能解释仿射二次曲面的积分对应物。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.