On the number of certain del Pezzo surfaces of degree four violating the Hasse principle

JOURNAL OF NUMBER THEORY

卷:162

Article

Jahnel, Joerg¹  Schindler, Damaris^2,3 

[1] Univ Siegen, Dept Math, Walter Flex Str 3, D-57068 Siegen, Germany

[2] Hausdorff Ctr Math, D-53115 Bonn, Germany

[3] Inst Adv Study, Einstein Dr 1, Princeton, NJ 08540 USA

关键词: Del Pezzo surface;    Hasse principle;    Brauer-Manin obstruction;   

DOI  :  10.1016/j.jnt.2015.10.018

来源: Elsevier

【 摘 要 】

We give an asymptotic expansion for the density of del Pezzo surfaces of degree four in a certain Birch Swinnerton-Dyer family violating the Hasse principle due to a Brauer Manin obstruction. Under the assumption of Schinzel's hypothesis and the finiteness of Tate Shafarevich groups for elliptic curves, we obtain an asymptotic formula for the number of all del Pezzo surfaces in the family, which violate the Hasse principle. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free