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

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arxiv 2310.16599 v2 pith:NT6MJYOU submitted 2023-10-25 math.AC

Kaito Kimura , Justin Lyle , Yuya Otake , Ryo Takahashi This is my paper · ORCID
classification math.AC
keywords operatornamelocalisolatedsingularitydepthhavingimplyequicharacteristic
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abstract

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

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Cited by 3 Pith papers

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