The stability of certain classes of uni-ruled varieties
We study the group of tame automorphisms of a smooth affine -dimensional quadric, which we can view as the underlying variety of . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in is linearizable, and that satisfies the Tits alternative.
L’auteur présente des applications élémentaires de la théorie du corps de classes de Kato et Parshin en dimensions 1 et 3 : calcul du conducteur d’une extension de Witt-Artin-Schreier d’un corps local de dimension 1, et étude des revêtements abéliens des surfaces.
We describe three-dimensional terminal toric flips. We obtain the complete local description of three-dimensional terminal toric flips.