Isotriviality and etale cohomology of Laurent polynomial rings

摘要

We provide a detailed study of torsors over Laurent polynomial rings under the action of an algebraic group. As applications we obtained variations of Raghunathan's results on torsors over affine space, isotriviality results for reductive group schemes and forms of algebras, and decomposition properties for Azumaya algebras. (c) 2007 Elsevier B.V. All rights reserved.