Markus Spitzweg (Osnabrück): From Tannakian to motivic categories

Abstract:
The envisioned abelian category of mixed motives over a field with rational coefficients should be a tannakian category following ideas of Grothendieck and Deligne. We will shortly review this concept and some universal properties of specific tannakian categories. Similar universal properties also make sense for stable categories. We will enlarge a corresponding result of Iwanari for the general linear group to orthogonal and symplectic groups and give applications to categories of etale motives.
This is joint work in progress with Hadrian Heine.