Purity in motivic homotopy theory

点击翻译按钮获取中文摘要

The aim of the project is to prove purity results within the Morel-Voevodsky motivic stable homotopy category, analogous to Gabber's purity results for etale cohomology. Such purity results are identifications of the operation i^! E with a suspension of the pullback i^* E, for suitable morphisms i of schemes and suitable motivic spectra E. Morphisms of interest are regular closed embeddings of regular schemes. Motivic spectra of relevance are the motivic Eilenberg-MacLane spectrum representing motivic cohomology with integer coefficients, the Thom spectrum representing algebraic cobordism, and the sphere spectrum. This supplies not only answers to a conjecture of Deglise, but also interesting computations of motivic cohomology, algebraic cobordism and stable homotopy groups via localization sequences.