We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over ℚ such that Br(S)/Br(ℚ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.
@article{bwmeta1.element.doi-10_2478_s11533-012-0042-6,
author = {Andreas-Stephan Elsenhans and J\"org Jahnel},
title = {On the order three Brauer classes for cubic surfaces},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {903-926},
zbl = {1276.11112},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0042-6}
}
Andreas-Stephan Elsenhans; Jörg Jahnel. On the order three Brauer classes for cubic surfaces. Open Mathematics, Tome 10 (2012) pp. 903-926. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0042-6/
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