Title: Symmetry in the vanishing of Ext over Gorenstein rings
Abstract: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...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 $R$, $\mathrm{Ext}^i_R(M,N)=0$ for all $i\gg 0$ if and only if $\mathrm{Ext}^i_R(N,M)=0$ for all $i\gg 0$.Read More