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Torsors under tori and Néron models

Torsors under tori and Néron models

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 …