On finite dimensionality of mixed Tate motives

Abstract

We prove a few results concerning the notions of finite dimensionality of mixed Tate motives in the sense of Kimura and O'Sullivan. It is shown that being oddly or evenly finite dimensional is equivalent to vanishing of certain cohomology groups defined by means of Levine weight filtration. We then explain the relation to the Grothendieck group of the triangulated category D of mixed Tate motives. This naturally gives rise to a λ-ring structure on K_0(D).