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On the Frequency of Algebraic Brauer Classes on Certain Log K3 Surfaces

Published online by Cambridge University Press:  03 December 2018

Jörg Jahnel
Affiliation:
Department Mathematik, Univ. Siegen, Walter-Flex-Str. 3, D-57068 Siegen, Germany Email: jahnel@mathematik.uni-siegen.de URL: http://www.uni-math.gwdg.de/jahnel
Damaris Schindler
Affiliation:
Mathematisch Instituut, Universiteit Utrecht, Budapestlaan 6, NL-3584 CD Utrecht, The Netherlands Email: d.schindler@uu.nl URL: http://www.uu.nl/staff/DSchindler
Corresponding

Abstract

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.

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© Canadian Mathematical Society 2018 

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Footnotes

The second author was supported by the NWO Veni Grant No. 016.Veni.173.016.

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