Let $A$ be a regular local ring and $I\subset A$ a complete intersection ideal.
We have the natural map $\delta:Hom_A(I,A/I)\rightarrow Ext_A^1(A/I,A/I)$.
For a given $\alpha\in Hom_A(I,A/I)$ is there an "explicit" description of a $A$-module $0\rightarrow A/I\rightarrow M\rightarrow A/I\rightarrow 0$ whose class is $\delta(\alpha)$?
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2$\begingroup$ Yes, push out the canonical extension of A/I by I along the given map I->A/I. Explicitly, $M=(A/I \oplus A)/R)$ with R generated by $(\alpha(f), -f)$ for all $f\in I$. $\endgroup$– Piotr AchingerCommented Jun 7, 2021 at 14:18
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$\begingroup$ Thank you very much. $\endgroup$– pi_1Commented Jun 7, 2021 at 14:43
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