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
.