Asymmetric complete resolutions and vanishing of Ext over Gorenstein rings

Details Asymmetric complete resolutions and vanishing of Ext over Gorenstein rings Asymmetric complete resolutions and vanishing of Ext over Gorenstein rings

2005-10-28

arxiv.org/abs/math/0510644v1

Mathematics

Commutative Algebra

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

Scientific paper

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 $i>0$.

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