Murre's conjectures and explicit Chow--Kuenneth projectors for some varieties

In this paper, we investigate Murre’s conjectures on the structure of rational Chow groups and exhibit explicit Chow–Kuenneth projectors for some examples. More precisely, the examples we study are the varieties which have a nef tangent bundle. For surfaces and threefolds which have a nef tangent bundle explicit Chow–Kuenneth projectors are obtained which satisfy Murre’s conjectures and the motivic Hard Lefschetz theorem is verified.