Martin Bright
Published 2009-11-25, updated 2010-11-15Version 2
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 XX/R is a model of X then, using a result of Brahm, we show that X-torsors under G extend to XX-torsors under a N\'eron 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 fibre to study the arithmetic of X.
Comments: 10 pages
Journal: Journal de Th\'eorie des Nombres de Bordeaux 23 (2011), 309-321
Rational points of the group of components of a Neron model
Corrigendum to Néron models, Lie algebras, and reduction of curves of genus one [LLR1] and The Brauer group of a surface [LLR2]
Néron models of $Pic^0$ via $Pic^0$
![QR code for arXiv:0911.4834 [math.AG]](http://oss.arxitics.com/images/favicon.svg)