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

Jörg Jahnel; Damaris Schindler

doi:10.1016/j.jnt.2015.10.018

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

Jörg Jahnel
, Damaris Schindler^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	224-254
Number of pages	31
Journal	Journal of Number Theory
Volume	162
DOIs	https://doi.org/10.1016/j.jnt.2015.10.018
Publication status	Published - 1 May 2016
Externally published	Yes

Keywords

Brauer-Manin obstruction
Del Pezzo surface
Hasse principle

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10.1016/j.jnt.2015.10.018

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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.",

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AU - Schindler, Damaris

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N2 - 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.

AB - 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.

KW - Brauer-Manin obstruction

KW - Del Pezzo surface

KW - Hasse principle

UR - https://www.scopus.com/pages/publications/84949908729

U2 - 10.1016/j.jnt.2015.10.018

DO - 10.1016/j.jnt.2015.10.018

M3 - Article

AN - SCOPUS:84949908729

SN - 0022-314X

VL - 162

SP - 224

EP - 254

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

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

Abstract

Keywords

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