The Tate-Shafarevich groups of multinorm-one tori

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Lee, T. Y.^1,2 

[1] Tech Univ Dortmund, Fak Math, Lehrstuhl LSVI, Vogelpothsweg 87, D-44227 Dortmund, Germany

[2] NTU MATH, Astron Math Bldg 5F,1,Sec 4,Roosevelt Rd, Taipei 10617, Taiwan

关键词: Multinorm;    Tori;    Tate-Shafarevich groups;    Local-global principles;    Weak approximation;    Brauer-Manin obstructions;   

DOI  :  10.1016/j.jpaa.2021.106906

来源: Elsevier

【 摘 要 】

Let k be a global field and L be a product of cyclic extensions of k. Let T be the torus defined by the multinorm equation N-L/k(x)=1 and let (T) over cap be its character group. The Tate-Shafarevich group and the algebraic Tate-Shafarevich group of (T) over cap in degree 2 give obstructions to the Hasse principle and weak approximation for rational points on principal homogeneous spaces T. We give concrete descriptions of these groups and provide several examples.

【 授权许可】

Free