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Article Dans Une Revue Journal of Pure and Applied Algebra Année : 2015

Polyhedral divisors and torus actions of complexity one over arbitrary fields

Kevin Langlois
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Résumé

We show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisors holds over an arbitrary field. We also describe a class of multigraded algebras over Dedekind domains. We study how the algebra associated to a polyhedral divisor changes when we extend the scalars. As another application, we provide a combinatorial description of affine $\mathbf{G}$-varieties of complexity one over a field, where $\mathbf{G}$ is a (not-nescessary split) torus, by using elementary facts on Galois descent. This class of affine $\mathbf{G}$-varieties is described via a new combinatorial object, which we call (Galois) invariant polyhedral divisor.
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Dates et versions

hal-00713400 , version 1 (30-06-2012)
hal-00713400 , version 2 (01-07-2012)
hal-00713400 , version 3 (02-05-2013)
hal-00713400 , version 4 (11-07-2014)
hal-00713400 , version 5 (16-06-2020)

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Kevin Langlois. Polyhedral divisors and torus actions of complexity one over arbitrary fields. Journal of Pure and Applied Algebra, 2015, 219 (6), ⟨10.1016/j.jpaa.2014.07.021⟩. ⟨hal-00713400v5⟩

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