  We study Gorenstein liaison of codimension two subschemes of an
arithmetically Gorenstein scheme X. Our main result is a criterion for two such
subschemes to be in the same Gorenstein liaison class, in terms of the category
of ACM sheaves on X. As a consequence we obtain a criterion for X to have the
property that every codimension 2 arithmetically Cohen-Macaulay subscheme is in
the Gorenstein liaison class of a complete intersection. Using these tools we
prove that every arithmetically Gorenstein subscheme of $\mathbb{P}^n$ is in
the Gorenstein liaison class of a complete intesection and we are able to
characterize the Gorenstein liaison classes of curves on a nonsingular quadric
threefold in $\mathbb{P}^4$.
