Diagonal quartic surfaces and transcendental elements of the Brauer group

DOI10.1017/S1474748010000149zbMath1263.14023arXiv0911.1268OpenAlexW2962830035MaRDI QIDQ3160686

Evis Ieronymou

Publication date: 8 October 2010

Published in: Journal of the Institute of Mathematics of Jussieu (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0911.1268

zbMATH Keywords

weak approximationBrauer groupBrauer-Manin obstructiondiagonal quartic surfaces

Mathematics Subject Classification ID

Varieties over global fields (11G35) Brauer groups of schemes (14F22) Global ground fields in algebraic geometry (14G25)

Related Items

Cohomology and the Brauer groups of diagonal surfaces ⋮ An example of a Brauer-Manin obstruction to weak approximation at a prime with good reduction ⋮ Odd torsion Brauer elements and arithmetic of diagonal quartic surfaces over number fields ⋮ Effective computation of Picard groups and Brauer-Manin obstructions of degree two \(K3\) surfaces over number fields ⋮ Effectivity of Brauer-Manin obstructions on surfaces ⋮ Failure of the Hasse principle for Enriques surfaces ⋮ Transcendental obstructions to weak approximation on general \(K3\) surfaces ⋮ Odd order Brauer-Manin obstruction on diagonal quartic surfaces ⋮ Arithmetic of K3 Surfaces ⋮ Finiteness theorems for K3 surfaces and abelian varieties of CM type ⋮ Transcendental Brauer groups of products of CM elliptic curves ⋮ On Brauer groups of double covers of ruled surfaces ⋮ Odd order obstructions to the Hasse principle on general K3 surfaces ⋮ A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold ⋮ Failure of the Hasse principle on general surfaces

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