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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...

Transversal crystals of finite level

Bernard Le Stum, Adolfo Quirós (1997)

Annales de l'institut Fourier

We extend Ogus’notion of T -crystal and F -span to the context of Berthelot’s crystals of level m and we study the generalization of Ogus’theorem on the equivalence between T -crystals and F -spans of width less than p .

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