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The Brauer-Manin obstruction on a general diagonal quartic surface

Martin Bright — 2011

Acta Arithmetica

Torsors under tori and Néron models

Martin Bright — 2011

Journal de Théorie des Nombres de Bordeaux

Let $R$ be a Henselian discrete valuation ring with field of fractions $K$ . If $X$ is a smooth variety over $K$ and $G$ a torus over $K$ , then we consider $X$ -torsors under $G$ . If $𝒳 / R$ is a model of $X$ then, using a result of Brahm, we show that $X$ -torsors under $G$ extend to $𝒳$ -torsors under a Néron model of $G$ if $G$ is split by a tamely ramified extension of $K$ . It follows that the evaluation map associated to such a torsor factors through reduction to the special fibre. In this way we can use the geometry of the special...

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