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This paper provides a method to get a noetherian equicharacteristic local UFDwith an isolated singularity from a given noetherian completeequicharacteristic local ring, preserving certain properties. This is appliedto invesitgate the (non)vanishing of Ext modules. It is proved that there exista Gorenstein local UFD $A$ having an isolated singularity such that$\operatorname{Ext}_A^{\gg0}(M,N)=0$ does not imply$\operatorname{Ext}_A^{\gg0}(N,M)=0$, a Gorenstein local UFD $B$ having anisolated singularity such that $\operatorname{Tor}_{>0}^B(M,N)=0$ does notimply $\operatorname{depth}(M\otimes_B N)=\operatorname{depth}M+\operatorname{depth} N-\operatorname{depth} B$, and a Cohen-Macaulay localUFD $C$ having an isolated singularity such that$\operatorname{Ext}_C^{>0}(M,C)=0$ does not imply the total reflexivity of $M$.

On the vanishing of Ext modules over a local unique factorization domain with an isolated singularity