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Let $P_1\overset{\partial}{\rightarrow} P_0\rightarrow M\rightarrow 0$ be an exact sequence of $A$-modules with $P_0$, $P_1$ finitely generated and projective. The transpose $T(M)$ is defined as $\mbox{coker}\mbox{Hom}(\partial,A)$, after applying $\mbox{Hom}(-,A)$: $0\leftarrow T(M)\leftarrow P_1^*\overset{\mbox{Hom}(\partial,A)}\longleftarrow P_0^*\leftarrow M^*\leftarrow0$ How does one show that $T(M)$ is independent, up to projective equivalence, on the choice of the projective resolution? Many books mention this fact but none of them seem to give a proof.

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    @Theo Buehler Yes, I saw that hint, but as is often the case with Eisenbud, I don't see how that can be of any help.2011-09-16

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I found an answer here:

http://arxiv.org/pdf/math/9809121v2