Theory of mixed motives and theory of scissors congruence groups of algebraic polyhedra

点击翻译按钮获取中文摘要

In paper 1 the triangulated category of mixed motives over a field D(k) was constructed. This theory has been conjectured to exist since the early 1980's. The theory is expected have much application. In paper 2, the existence of an appropriate t-structure on D(k) has been studied assuming some "standard conjectures". I showed how to associate to a projective variety its motive, an object of D(k), in paper 3. We explored the motivic analogue of the "decomposition theorem" for the direct image of the constant sheaf under a proper map, paper 4. This includes the framework of motivic sheaves over an arbitrary variety.In paper 5, Hanamura and M.Yoshida studied Hodge theory on twisted cohomology, and applied it to derive the analogue of Riemann's inequality.