  In this article, we study the relative negative K-groups $K_{-n}(f)$ of a map
$f: X \to S $ of schemes. We prove a relative version of the Weibel conjecture
i.e. if $f: X \to S$ is a smooth affine map of noetherian schemes with $\dim
S=d$ then $K_{-n}(f)=0$ for $n> d+1$ and the natural map $K_{-n}(f) \to
K_{-n}(f \times \mathbb{A}^{r})$ is an isomorphism for all $r>0$ and $n>d.$ We
also prove a vanishing result for relative negative K-groups of a subintegral
map.

Algebraic Geometry;K-Theory and Homology