Arithmetic of del Pezzo surfaces of degree 4 and vertical Brauer groups

DOI10.1016/j.aim.2014.01.004zbMath1329.14051OpenAlexW2054859179MaRDI QIDQ2445918

Anthony Várilly-Alvarado, Bianca Viray

Publication date: 15 April 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2014.01.004

zbMATH Keywords

Brauer-Manin obstructiondegree 4 del Pezzo surfacesvertical Brauer groups

Mathematics Subject Classification ID

Rational points (14G05) Brauer groups of schemes (14F22)

Related Items (9)

Del Pezzo surfaces of degree four violating the Hasse principle are Zariski dense in the moduli scheme ⋮ Rational points on Del Pezzo surfaces of degree four ⋮ Vanishing of the Brauer group of a del Pezzo surface of degree 4 ⋮ On integral points on degree four del Pezzo surfaces ⋮ Quadratic points on intersections of two quadrics ⋮ On the number of certain del Pezzo surfaces of degree four violating the Hasse principle ⋮ Anticanonical codes from del Pezzo surfaces with Picard rank one ⋮ On the algebraic Brauer classes on open degree four del Pezzo surfaces ⋮ Genus one fibrations and vertical Brauer elements on del Pezzo surfaces of degree 4

Uses Software

• Magma

Cites Work

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• Algebraic families of nonzero elements of Shafarevich-Tate groups
• Descent on fibrations over the projective line
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• The Hardy–Littlewood conjecture and rational points

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