Integral points on twisted Markoff surfaces

JOURNAL OF NUMBER THEORY

卷:220

Article

Chen, Sheng¹ 

[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

关键词: Brauer group;    Brauer-Manin obstruction;    Group cohomology;    Integral point;    Hasse principle;   

DOI  :  10.1016/j.jnt.2020.06.012

来源: Elsevier

【 摘 要 】

We study the integral Hasse principle for affine varieties of the shape ax(2) + y(2) + z(2) - xyz = m, using the Brauer-Manin obstruction, and we produce examples whose Brauer groups include 4-torsion elements. We describe these elements explicitly, and in some cases, we show that there is no Brauer-Manin obstruction to the integral Hasse principle for them. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free