Murthy's splitting conjecture

Let $R$ be a smooth affine algebra of Krull dimension $d\geq 3$ over an algebraically closed field. Let $P$ be a projective $R$-module of rank $d-1$. Murthy's splitting conjecture. The top Chern class

$$c_{d-1}(P)=0$$

in $CH^{d-1}(\operatorname{Spec}(R))$ if and only if

$$P\cong Q\oplus R$$

for some $R$-module $Q$. Murthy's splitting conjecture generalizes Murthy's result in rank equal to the dimension and remains open in general.