Geodesic
On the Frequency of Algebraic Brauer Classes on Certain Log K3 Surfaces
Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 551-563

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DOI

Given systems of two (inhomogeneous) quadratic equations in four variables, it is known that the Hasse principle for integral points may fail. Sometimes this failure can be explained by some integral Brauer–Manin obstruction. We study the existence of a non-trivial algebraic part of the Brauer group for a family of such systems and show that the failure of the integral Hasse principle due to an algebraic Brauer–Manin obstruction is rare, as for a generic choice of a system the algebraic part of the Brauer-group is trivial. We use resolvent constructions to give quantitative upper bounds on the number of exceptions.
DOI : 10.4153/S0008439518000590
Mots-clés : Brauer classes, Brauer–Manin obstruction, log K3 surfaces 
Jahnel, Jörg; Schindler, Damaris. On the Frequency of Algebraic Brauer Classes on Certain Log K3 Surfaces. Canadian mathematical bulletin, Tome 62 (2019) no. 3, pp. 551-563. doi: 10.4153/S0008439518000590
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     title = {On the {Frequency} of {Algebraic} {Brauer} {Classes} on {Certain} {Log} {K3} {Surfaces}},
     journal = {Canadian mathematical bulletin},
     pages = {551--563},
     year = {2019},
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     doi = {10.4153/S0008439518000590},
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