Murre's conjectures and explicit Chow–Kunneth projectors for varieties with a nef tangent bundle

Abstract

In this paper, we investigate Murre's conjectures on the structure of rational Chow groups and exhibit explicit Chow-Künneth 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-Kunneth projectors are obtained which satisfy Murre's conjectures, and the motivic Hard Lefschetz theorem is verified.