Orientations of MW-Motives
Time: Mon, 21 Oct 2019, 15:30-17:00
Place: Third conference room at floor 2, Jinchunyuan West Building (近春园西楼)
Speaker: Nanjun Yang (YMSC, Tsinghua University)
Abstract:
The category of (stable) MW-motives (defined by B. Calmès, F. Déglise and J. Fasel) is a refined version of Voevodsky’s big motives, which provides a better approximation to the stable homotopy category of Morel and Voevodsky. A significant characteristic of this theory is that the projective bundle theorem doesn’t hold.
In this talk, we introduce Milnor-Witt K-theory and Chow-Witt rings, which leads to the definition of (stable/effective) MW-motives over smooth bases. Then we discuss their quarternionic projective bundle theorem and Gysin triangles. As an application, we compute the Hom-groups between proper smooth schemes in the category of MW-motives.