Intersection complex of any threefold as a Chow motive

Abstract

Motivated by the characterization of the intersection complex in terms of S$.$Morel's weight truncations, we introduced an object $EM^{F}_{X}$ in the setting of motivic sheaves for certain schemes $X$ and weight profiles $F$. In this article, we show that when $X$ is any threefold, this object satisfies Wildeshaus's characterization of a motivic intersection complex. In particular, we demonstrate that the construction is a suitably functorial Chow motive lifting the motivic intersection complex for an arbitrary threefold.