Homological and motivic invariants of torsorsTools Tanania, Fabio (2020) Homological and motivic invariants of torsors. PhD thesis, University of Nottingham.
AbstractMany 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, SeveriBrauer 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 StiefelWhitney classes, by computing the motivic cohomology of the Nisnevich classifying spaces of orthogonal groups, with the purpose of studying quadratic forms.
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