Abstract
Let $k$ be a perfect field which admits resolution of singularities in the sense of Friedlander and Voevodsky (for example, $k$ of characteristic 0). Let $X$ be a smooth proper $k$-variety of pure dimension $n$ and $Y,Z$ two disjoint closed subsets of $X$. We prove an isomorphism \[ \displaystyle M(X-Z,Y)\simeq M(X-Y,Z)^*(n)[2n],\] where $M(X-Z,Y)$ and $M(X-Y,Z)$ are relative Voevodsky motives, defined in his triangulated category $\operatorname{DM}_{\rm gm}(k)$.
