Asymmetric complete resolutions and vanishing of Ext over Gorenstein rings

Abstract

We construct a class of Gorenstein local rings $R$ which admit minimal complete $R$-free resolutions $\bd C$ such that the sequence $\{\rank_R C_i\}$ is constant for $i<0$, and grows exponentially for all $i>0$. Over these rings we show that there exist finitely generated $R$-modules $M$ and $N$ such that $\Ext^i_R(M,N)=0$ for all $i>0$, but $\Ext^i_R(N,M)\ne 0$ for all $i>0$.

14 pages, to appear in Internat. Math. Res. Notices