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Let $A$ be a local Gorenstein $\mathbb{C}$-algebra (not necessarily regular). Let $M,N$ be maximal Cohen-Macaulay $A$-modules. Is Hom(M,N) a maximal Cohen-Macaulay A-module?

Note that I had asked this question on stackexchange, but did not get an answer.

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  • $\begingroup$ No, that is not true. Let $A$ be $\mathbb{C}[[s,t]/\langle st \rangle$, let $M$ be $A/\langle s \rangle$, and let $N$ be $A/\langle t \rangle$. Then $\text{Hom}_A(M,N)$ is the zero module. $\endgroup$
    – Jason Starr
    Commented 4 hours ago

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