  We investigate symmetry in the vanishing of Ext for finitely generated
modules over local Gorenstein rings. In particular, we define a class of local
Gorenstein rings, which we call AB rings, and show that for finitely generated
modules $M$ and $N$ over an AB ring $R$, $Ext^i_R(M,N)=0$ for all $i >> 0$ if
and only if $Ext^i_R(N,M)=0$ for all $i >> 0$.
