Principes locaux-globaux pour certaines fibrations en torseurs sous un tore

© Cambridge Philosophical Society 2014. Let k be a number field and T a k-torus. Consider a family of torsors under T, i.e. a morphism f : X → double-struck Pk1 from a projective, smooth k-variety X to double-struck Pk1, the generic fibre Xη → η of which is a smooth compactification of a principal homogeneous space under T ⊗k η. We study the Brauer-Manin obstruction to the Hasse principle and to weak approximation for X, assuming Schinzel's hypothesis. We generalise Wei's recent results [21]. Our results are unconditional if k = Q and all non-split fibres of f are defined over Q. We also establish an unconditional analogue of our main result for zero-cycles of degree 1.

Publication year:2015

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Authors from:Higher Education

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