  We show that the existence of locally finite stability conditions on the
bounded derived category $\mathbf{D}^{b}(X)$ of coherent sheaves on an affine
Noetherian scheme $X$ is equivalent to $\dim X=0$. We also study the spaces of
stability conditions on the category of morphisms $\mathbf M_{X}$ in the
derived category of the scheme $X$ and show that the spaces of stability
conditions on $\mathbf{D}^{b}(X)$ and $\mathbf{M}_{X}$ are homotopy equivalent
to each other.
