Brauer groups of diagonal quartic surfaces

Authors:
Martin Bright
Affiliations:
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom
Venue:
Journal of Symbolic Computation
Year:
2006

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Abstract

We describe explicit methods of exhibiting elements of the Brauer groups of diagonal quartic surfaces. Using these methods, we compute the algebraic Brauer-Manin obstruction in two contrasting examples. In the second example, the obstruction is found to be trivial but a computer search reveals no points of small height on the surface.