Homological and motivic invariants of torsors - Tanania, Fabio (2020)
Many interesting objects in algebraic geometry arise as torsors of linear algebraic groups over a field. Some notable examples are provided by vector bundles, quadratic forms, Hermitian forms, octonion algebras, Severi-Brauer varieties and many others. The main aim of this thesis is to investigate torsors from a motivic homotopic perspective, by using Nisnevich classifying spaces and their characteristic classes. In order to do so, we will need a Gysin long exact sequence induced by fibrations with motivically invertible reduced fiber. The leading example is provided by the work of Smirnov and Vishik where they introduce subtle Stiefel-Whitney classes, by computing the motivic cohomology of the Nisnevich classifying spaces of orthogonal groups, with the purpose of studying quadratic forms.