Rational points on del Pezzo surfaces of degree four

Vladimir Mitankin; Cecília Salgado

doi:10.1142/S179304212250107X

Rational points on del Pezzo surfaces of degree four

Vladimir Mitankin^*, Cecília Salgado

^*Corresponding author for this work

Algebra

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Abstract

We study the distribution of the Brauer group and the frequency of the Brauer-Manin obstruction to the Hasse principle and weak approximation in a family of smooth del Pezzo surfaces of degree four over the rationals. We also study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.

Original language	English
Pages (from-to)	2099-2127
Number of pages	29
Journal	International Journal of Number Theory
Volume	18
Issue number	9
DOIs	https://doi.org/10.1142/S179304212250107X
Publication status	Published - 1-Jul-2022

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title = "Rational points on del Pezzo surfaces of degree four",

abstract = "We study the distribution of the Brauer group and the frequency of the Brauer-Manin obstruction to the Hasse principle and weak approximation in a family of smooth del Pezzo surfaces of degree four over the rationals. We also study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.",

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T1 - Rational points on del Pezzo surfaces of degree four

AU - Mitankin, Vladimir

AU - Salgado, Cecília

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N2 - We study the distribution of the Brauer group and the frequency of the Brauer-Manin obstruction to the Hasse principle and weak approximation in a family of smooth del Pezzo surfaces of degree four over the rationals. We also study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.

AB - We study the distribution of the Brauer group and the frequency of the Brauer-Manin obstruction to the Hasse principle and weak approximation in a family of smooth del Pezzo surfaces of degree four over the rationals. We also study the geometry and arithmetic of a genus one fibration with two reducible fibres for which a Brauer element is vertical.

U2 - 10.1142/S179304212250107X

DO - 10.1142/S179304212250107X

M3 - Article

SN - 1793-0421

VL - 18

SP - 2099

EP - 2127

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 9

ER -

Rational points on del Pezzo surfaces of degree four

Abstract

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