Article ID Journal Published Year Pages File Type
6415342 Journal of Number Theory 2016 31 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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