28 research outputs found

    Cohomology and the Brauer groups of diagonal surfaces

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    We present a method for calculating the Brauer group of a surface given by a diagonal equation in the projective space. For diagonal quartic surfaces with coefficients in Q we determine the Brauer groups over Q and Q(i).Comment: 45 page

    On the Brauer group of diagonal quartic surfaces

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    We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over Q to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D by the image of the Brauer group of Q. The proof is based on the isomorphism of the Fermat quartic surface with a Kummer surface due to Masumi Mizukami.Comment: Appendix "The Fermat quartic as a Kummer surface (after Mizukami)", by Sir Peter Swinnerton-Dye

    Transcendental obstructions to weak approximation on general K3 surfaces

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    We construct an explicit K3 surface over the field of rational numbers that has geometric Picard rank one, and for which there is a transcendental Brauer-Manin obstruction to weak approximation. To do so, we exploit the relationship between polarized K3 surfaces endowed with particular kinds of Brauer classes and cubic fourfolds.Comment: 24 pages, 3 figures, Magma scripts included at the end of the source file

    Contents of Volume 41

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